@String{mi = "Mathematisches Institut, Universit{\"a}t zu K{\"o}ln"} @String{miaddress = "Weyertal 86-90, 50931 K{\"o}ln, Germany"} @String{inf = "Informatik, Universit{\"a}t zu K{\"o}ln"} @String{infaddress = "Pohligstr. 1, 50969 K{\"o}ln, Germany"} @String{dlr = "Deutsches Zentrum f{\"u}r Luft- und Raumfahrt"} @String{acyb = "Acta Cybernetica"} @String{actainf = "Acta Informatica"} @String{advam = "Advances in Applied Mathematics"} @String{algrc = "Algorithmica"} @String{apml = "Applied Mathematics Letters"} @String{anor = "Annals of Operations Research"} @String{amai = "Annals of Mathematics and Artificial Intelligence"} @String{adm = "Archiv der Mathematik"} @String{arsc = "Ars Combinatoria"} @String{c = "Combinatorica"} @String{comgeo = "Computational Geometry"} @String{compoa = "Computational Optimization and Applications"} @String{comptng = "Computing"} @String{dacgeom = "Discrete & Computational Geometry"} @String{dm = "Discrete Mathematics"} @String{dam = "Discrete Applied Mathematics"} @String{ejoc = "European Journal of Combinatorics"} @String{ejor = "European Journal of Operational Research"} @String{fgcs = "Future Generation Computer Systems"} @String{gammm = "GAMM-Mitteilungen"} @String{geomded = "Geometriae Dedicata"} @String{infspec = "Informatik-Spektrum"} @String{ijcga = "International Journal of Computational Geometry and Applications"} @String{ijgt = "International Journal of Game Theory"} @String{ijmpc = "International Journal of Modern Physics C"} @String{ipl = "Information Processing Letters"} @String{inf_spec = "Informatik-Spektrum"} @String{jdpI = "Journal de Physique I"} @String{jalgo = "Journal of Algorithms"} @String{jcompbio = "Journal of Computational Biology"} @String{jocta = "Journal of Combinatorial Theory A"} @String{joctb = "Journal of Combinatorial Theory B"} @String{jogaa = "Journal of Graph Algorithms and Applications"} @String{jogt = "Journal of Graph Theory"} @String{jphysa = "Journal of Physics A: Mathematical and General"} @String{manmath = "manuscripta mathematica"} @String{matprog = "Mathematical Programming"} @String{nucla = "Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment"} @String{offsys = "Offene Systeme"} @String{orletters = "Operations Research Letters"} @String{orspektrum = "OR-Spektrum"} @String{parco = "Parallel Computing"} @String{physa = "Physica A"} @String{pre = "Physical Review E"} @String{rsaa = "Random Structures & Algorithms"} @String{sicon = "SIAM Journal on Control and Optimization"} @String{tcad = "IEEE Transactions on COMPUTER-AIDED DESIGN of Integrated Circuits and Systems"} @String{zamm = "Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik"} @String{zor = "Zeitschrift f{\"u}r Operations Research"} @TechReport{zpr99-374, author = "M. J{\"u}nger and S. Leipert", institution = inf, title = "Level Planar Embedding in Linear Time (Full Version)", crindex = "354k,47,zpr99-374.ps.gz", year = "1999", keywords = "Level Planararity, Level Planar Embedding, PQ-Trees, Graph Drawing; 05C85, 68R10, 90C35", annote = "A level graph $G = (V,E,\lev)$ is a directed acyclic graph with a mapping $\lev : V \rightarrow \{1,2,\dots,k\}$, $k \ge 1$, that partitions the vertex set $V$ as $V = V^1\cup V^2\cup\dots\cup V^k$, $V^j = \lev^{-1}(j)$, $V^i \cap V^j = \emptyset$ for $i\ne j$, such that $\lev(v) \ge \lev(u) +1$ for each edge $(u,v) \in E$. The level planarity testing problem is to decide if $G$ can be drawn in the plane such that for each level $V^i$, all $v \in V^i$ are drawn on the line $l_i = \{(x,k-i) \mid x \in \mathbb{R}\}$, the edges are drawn monotonically with respect to the vertical direction, and no edges intersect except at their end vertices.
In order to draw a level planar graph without edge crossings, a level planar embedding of the level graph has to be computed. Level planar embeddings are characterized by linear orderings of the vertices in each $V^i$ ($1\le i\le k$). We present an $\order(|V|)$ time algorithm for embedding level planar graphs. This approach is based on a level planarity test by J{\"u}nger, Leipert, Mutzel 1999.", } @InProceedings{zpr99-373, author = "S. Rosswog and P. Wagner", institution = dlr, title = "``Car-{SPH}´´: {A} Lagrangian Particle Scheme fot the Solution of the Macroscopic Traffic Flow Equations", booktitle = "to appear: Proc. Traffic and Granular Flow 1999", crindex = "73k,6,zpr99-372.ps.gz", year = "1999", keywords = "traffic simulation, traffic flow model, differential equations, particle scheme;", annote = "A Lagrangian particle scheme for the solution of the macroscopic traffic flow equations is presented. The scheme transforms the partial Navier-Stokes-like differential equations into a set of ordinary differential equations that are given as sums over particle contributions.
The continuity equation is fulfilled automatically by construction. The method is applied to the 'standard scenario' of a road loop where the traffic flow is governed by the macroscopic equations of Kerner and Konhaeuser.", } @Article{zpr99-372, author = "S. Rosswog and C. Gawron and S. Hasselberg and R. B{\"o}ning and P. Wagner", institution = dlr, title = "Computational Aspects in Traffic Simulation Problems", journal = "to appear: Future Generation Computer System", note = "Proc. High Performance Computing and Networking 1999", year = "1999", crindex = "1115k,9,zpr99-372.ps.gz", keywords = "traffic simulation, dynamic traffic assignment, dynamic user equilibrium, shortest paths in street networks, improved Dijkstra-algorithm;", annote = "We discuss topics related to the notion of shortest paths in large street networks. In a first section we discuss the dynamic traffic assignment problem and describe an algorithm designed to determine user equilibria in simulation-based traffic models. The proposed algorithm is able to find in a reasonable amount of time equilibria in problems that are not treatable with conventional methods (e.g. Frank-Wolfe algorithm).
The second part deals with an improved algorithm to find shortest paths in street networks with given link cost functions. The main idea is to reduce the network using the intrinsic properties of street networks and to perform a (backward) Dijkstra-algorithm on this reduced network. This approach results in a highly accurate algorithm which is faster than the straight forward approach by a factor of four.", } @InProceedings{zpr99-371, author = "M. Hayer and W. Hochst{\"a}ttler", institution = mi, title = "Test Sets for Vertex Cover Problems (Extended Abstract)", booktitle = "Proc. 6th Twente Workshop on Graphs and Combinatorial Optimization", editor = "H. J. Broersma and U. Faigle and C. Hoede and J. L. Hurink", series = "Electronic Notes in Discrete Mathematics", volume = "3", crindex = "569k,5,zpr99-371.ps.gz", publisher = "Elsevier", year = "1999", annote = "We describe the structure of the unique minimal test set T for a family of vertex cover problems. The set T corresponds to the Gröbner basis of the binomial ideal for the problem as described in B. Conti and C. Traverso [Buchberger Algorithm and Integer Programming, LNCS 539, Springer (1991), 130-139]. While T has a surprisingly simple structure, in particular when the underlying graph is complete, it is NP-complete to decide whether the test set contains an improving element for a given feasible solution in the case of a complete graph.", } @PhdThesis{zpr99-370, author = "A. Erdmann", institution = inf, title = "Combinatorial Optimization Problems arising in Airline Industry", keywords = "Column generation, Dantzig-Wolfe decomposition, network design, constrained shortest path algorithm, crew pairing, set partitioning", pages = "106", year = "1999", } @TechReport{zpr99-369, author = "M. J{\"u}nger and S. Leipert and P. Mutzel", institution = inf, title = "Level Planarity Testing in Linear Time (Full Version)", year = "1999", crindex = "184k,37,zpr99-369.ps.gz", keywords = "Level Planar Graph, Level Planar Embedding, Hierarchy, PQ-Tree; 05C85, 68R10, 90C35", annote = "A level graph $G = (V,E,\lev)$ is a directed acyclic graph with a mapping $\lev : V \rightarrow \{1,2,\dots,k\}$, $k \ge 1$, that partitions the vertex set $V$ as $V = V^1\cup V^2\cup\dots\cup V^k$, $V^j = \lev^{-1}(j)$, $V^i \cap V^j = \emptyset$ for $i\ne j$, such that $\lev(v) \ge \lev(u) +1$ for each edge $(u,v) \in E$. The level planarity testing problem is to decide if $G$ can be drawn in the plane such that for each level $V^i$, all $v \in V^i$ are drawn on the line $l_i = \{(x,k-i) \mid x \in \R\}$, the edges are drawn monotone with respect to the vertical direction, and no edges intersect except at their end vertices. If $G$ has a single source, the test can be performed in $\order(|V|)$ time by an algorithm of DiBattista and Nardelli (1988) that uses the $PQ$-tree data structure introduced by Booth and Lueker (1976). $PQ$-trees have also been proposed by Heath and Pemmaraju (1995,1996) to test level planarity of level directed acyclic graphs with several sources and sinks. It has been shown in J{\"u}nger Leipert and Mutzel (1997) that this algorithm is not correct in the sense that it does not state correctly level planarity of every level planar graph. In this paper, we present a correct linear time level planarity testing algorithm that is based on two main new techniques that replace the incorrect crucial parts of the algorithm of Heath and Pemmaraju (1995,1996).", } @TechReport{zpr99-368, author = "C. Buchheim and M. J{\"u}nger and S. Leipert", institution = inf, title = "A Fast Layout Algorithm for k-Level Graphs", crindex = "128k,23,zpr99-368.ps.gz", year = "1999", keywords = "Sugiyama Algorithm, Hierarchies, Graph Drawing; 05C85, 68R10, 90C35", annote = "In this paper, we present a fast layout algorithm for k-level graphs with given permutations of the vertices on each level. The algorithm can be used in particular as a third phase of the Sugiyama algorithm (1981). The Sugiyama algorithm computes a layout for an arbitrary graph by (1) converting it into a k-level graph, (2) reducing the number of edge crossings by permuting the vertices on the levels, and (3) assigning y-coordinates to the levels and x-coordinates to the vertices. In the layouts generated by our algorithm, every edge will have at most two bends, and will be drawn vertically between these bends.", } @PhdThesis{zpr99-367, author = "F. Brockners", institution = inf, title = "Flu{\ss}steuerung f{\"u}r verl{\"a}{\ss}liche Multicastkommunication im Internet", pages = "178", year = "1999", publisher = "Shaker-Verlag", } @PhdThesis{zpr99-366, author = "C. Gawron", institution = inf, title = "Simulation-Based Traffic Assignment -- Computing User Equilibria in Large Street Networks", crindex = "1600k,113,zpr99-366.ps.gz", pages = "113", year = "1999", } @TechReport{zpr99-363, author = "U. Faigle and W. Kern and J. Kuipers", institution = mi, title = "On the computation of the nucleolus of a cooperative game", keywords = "core, nucleolus, prekernel, kernel, computational complexity, convex games, MCST-games, ellipsoid method; 90C27, 90D12", annote = "We consider classes of cooperative games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation.
In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel.", } @TechReport{zpr99-362, author = "U. Faigle and W. Kern", institution = mi, title = "An algebraic framework for the greedy algorithm with applications to the core and Weber set of cooperative games", year = "1999", keywords = "Antimatroid, cooperative game, core, greedy algorithm, matroid, Monge algorithm, poset, submodular, Weber set; 90C27, 90D12", annote = "An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in Rn. This model unifies various generalizations of combinatorial models in which the greedy algorithm and the Monge algorithm are successful and generalizations of the notions of core and Weber set in cooperative game theory.

As a further application, we show that an earlier model of ours as well as the algorithmic model of Queyranne, Spieksma and Tardella for the Monge algorithm can be treated within the framework of usual matroid theory (on unordered ground-sets), which permits also the efficient algorithmic solution of the intersection problem within this model.", } @TechReport{zpr99-361, author = "U. Faigle and W. Kern and D. Paulusma", institution = mi, title = "Note on the computational complexity of least core concepts for min-cost spanning tree games", keywords = "cooperative game, least core, nucleolus, spanning tree, NP-hard; 90C27, 90D12", annote = "Various least core concepts including the classical least core of cooperative games are discussed. By a reduction from minimum cover problems, we prove that computing an element in these least cores is in general $NP$-hard for minimum cost spannning tree games. As a consequence, computing the nucleolus, the nucleon and the per-capita nucleolus of minimum cost spanning tree games is also $NP$-hard.", } @Article{zpr99-360, author = "M. Hunting and U. Faigle and W. Kern", institution = mi, title = "A Lagrangian relaxation approach to the edge-weighted clique problem", year = "1999", keywords = "clique polytope, cut polytope, cutting plane, Boolean quadric polytope, quadratic knapsack polytope, Lagrangian relaxation; 90C27 90D12", journal = "to appear: European Journal of Operational Research", annote = "The $b$-clique polytope $CP^n_b$ is the convex hull of the node and edge incidence vectors of all subcliques of size at most $b$ of a complete graph on $n$ nodes. Including the Boolean quadric polytope $QP^n=CP^n_n$ as a special case and being closely related to the quadratic knapsack polytope, it has received considerable attention in the literature. In particular, the max-cut problem is equivalent with optimizing a linear function over $CP^n_n$. The problem of optimizing linear functions over $CP^n_b$ has so far been approached via heuristic combinatorial algorithms and cutting-plane methods.

We study the structure of $CP^n_b$ in further detail and present a new computational approach to the linear optimization problem based on the idea of integrating cutting planes into a Lagrangian relaxation of an integer programming problem that Balas and Christofides had suggested for the traveling salesman problem. In particular, we show that the separation problem for tree inequalities becomes polynomial in our Lagrangian framework. Finally, computational results are presented.", } @TechReport{zpr99-359, author = "M. B{\"o}hm", institution = inf, title = "Parallel {ABACUS} - Implementation", crindex = "145k,105,zpr99-359.ps.gz", keywords = "Parallel Programming, Branch&Cut, ABACUS; 68N", year = "1999", annote = "This document contains the C++ source code of the parallel extensions to the ABACUS system.", } @TechReport{zpr99-358, author = "M. B{\"o}hm", institution = inf, title = "Parallel {ABACUS} - Introduction and Tutorial", crindex = "67k,11,zpr99-358.ps.gz", keywords = "Parallel Programming, Branch&Cut, ABACUS; 68R, 90C, 90-01", year = "1999", annote = "This document describes the current state of the parallel version of ABACUS (version 2.3 beta). It should serve as an introduction to the design of the system as well as a tutorial for the user. The tutorial section describes how to extend and run the ABACUS example application in a parallel environment.", } @TechReport{zpr99-357, author = "M. J{\"u}nger and S. Leipert", institution = inf, title = "Level Planar Embedding in linear Time (Extended Abstract)", crindex = "115k,10,zpr99-357.ps.gz", keywords = "Level Planar Graph, Level Planar Embedding, Hierarchy, PQ-Tree; 05C85, 68R10, 90C35", annote = "In a level directed acyclic graph $G = (V,E)$ the vertex set $V$ is partitioned into $k \le |V|$ levels $V^1,V^2,\dots,V^k$ such that for each edge $(u,v) \in E$ with $u \in V^i$ and $v \in V^j$ we have $i In order to draw a level planar graph without edge crossings, a level planar embedding of the level graph has to be computed. Level planar embeddings are characterized by linear orderings of the vertices in each $V^i$ ($1\le i\le k$). We present an $\order(|V|)$ time algorithm for embedding level planar graphs. This approach is based on a level planarity test by J{\"u}nger, Leipert, and Mutzel 1998.", } @InCollection{zpr99-356, author = "E. Dahlhaus", institution = mi, title = "Minimal Elimination Ordering Inside a Given Chordal Graph", booktitle = "Graph-theoretic concepts in computer science, Proc. of the 23rd international workshop, WG '97, (Berlin, 1997)", editor = "R. H. Moehring", series = "Lecture Notes in Computer Science", volume = "1335", pages = "132--143", publisher = "Springer-Verlag", crindex = "97k,15,zpr99-356.ps.gz", keywords = "Gauss elimination, sparse matrices, chordal graphs, nested dissection, minimum degree heuristics; 68Q20, 68Q25, 68R10, 65F50", annote = "We consider the following problem, called Relative Minimal Elimination Ordering. Given a graph G=(V,E) which is a subgraph of the chordal graph G'=(V,E'), compute an inclusion minimal chordal graph G''=(V,E''), such that $E \subseteq E'' \subseteq E'$. We show that this can be done in O(nm) time. This extends the results of Telle. The algorithm is based only on well known results on chordal graphs.

This is an extended version of the paper published in WG 97.", } @Article{zpr99-355, author = "E. Dahlhaus", institution = mi, title = "Minimum Fill-in and Treewidth for Graphs Modularly Decomposable into Chordal Graphs", crindex = "76k,11,zpr99-355.ps.gz", keywords = "Modular decomposition, chordal graphs, minimum fill-in, efficient algorithms; 05C75, 05C85, 68Q25, 68R10", journal = "submitted to Discrete Applied Mathematics", year = "1999", annote = "We show that a minimum fill-in ordering of a graph can be determined in linear time if it can be modularly decomposed into chordal graphs. This generalizes results of L. Babel: Triangulating Graphs with few P4s. We show that the treewidth of these graphs can be determined in $O((n+m)\log n)$ time.", } @InProceedings{zpr99-355a, author = "E. Dahlhaus", institution = mi, title = "Minimum Fill-In and Treewidth for Graphs Modularly Decomposable into Chordal Graphs", booktitle = "Graph-Theoretic Concepts in Computer Science. Proc. of the 24th international workshop, WG '98, Smolenice Castle, Slovak Republic, June 18--20, 1998.", editor = "J. Hromkovic and O. Sykora", series = "Lecture Notes in Computer Science", volume = "1517", publisher = "Springer-Verlag", pages = "351--358", year = "1998", keywords = "Modular decomposition, chordal graphs, minimum fill-in, efficient algorithms; 05C75, 05C85, 68Q25, 68R10", } @Article{zpr99-354, author = "E. Dahlhaus", institution = mi, title = "Minimal Elimination Ordering for Graphs of Bounded Degree", crindex = "71k,10,zpr99-354.ps.gz", keywords = "Graph algorithms, chordal graphs, graph elimination, sparse matrices; 68R10, 68Q25", journal = "submitted to Discrete Applied Mathematics", annote = "We show that for graphs of bounded degree, a subset minimal elimination ordering can be determined in almost linear time.", } @TechReport{zpr99-353, author = "E. Dahlhaus", institution = mi, title = "An Improved Linear Time Algorithm for Minimal Elimination Ordering in Planar Graphs that is Parallelizable", crindex = "74k,10,zpr99-353.ps.gz", keywords = "parallel algorithms, graph algorithms, planar graphs; 68R10, 68Q22, 68Q25", journal = "submitted to WG 99", year = "1999", annote = "We present an alternative linear time algorithm that computes an ordering that produces a fill-in that is minimal with respect to the subset relation. It is simpler than an earlier algorithm of the author and is easily parallelizable. The algorithm does not rely on the computation of a breadth-first search tree.", } @InProceedings{zpr99-352a, author = "A. Nolte and R. Schrader", institution = mi, title = "Coloring in Sublinear Time", booktitle = "Algorithms - ESA '97, 5th Annual European Symposium", location = "Graz, Austria", editors = "R. Burkard and G. J. Woeginger", series = "Lecture Notes in Computer Science", volume = "1284", publisher = "Springer-Verlag", pages = "388--401", year = "1997", } @Article{zpr99-352, author = "A. Nolte and R. Schrader", institution = mi, title = "Coloring in Sublinear Time", keywords = "Simulated Annealing, inhomogeneous Markov chain, graph coloring", journal = "submitted to Discrete Applied Mathematics", year = "1999", crindex = "131k,30,zpr98-352.ps.gz", annote = "We will present an algorithm, based on SA-techniques and a sampling procedure, that colors a given random 3-colorable graph with high probability in sublinear time. This result is the first theoretical justification of many excellent experimental performance results of Simulated Annealing applied to graph coloring problems.", } @Article{zpr99-351, author = "A. Erdmann and A. Nolte and A. Noltemeier and R. Schrader", institution = inf, title = "Modeling and Solving the Airline Schedule Generation Problem", keywords = "Capacitated network design, Dantzig-Wolfe decomposition, set partitioning, set packing, Branch-and-Cut", note = "submitted to: Math. in Industrial Systems", year = "1999", crindex = "122k,23,zpr98-351.ps.gz", annote = "Since opening a new flight connection or closing an existing flight has a great impact on the revenues of an airline, the generation of the flight schedule is one of the fundamental problems in airline planning processes.
In this paper we concentrate on a special case of the problem. In contrast to airlines operating on regular schedules, the market for charter airlines is well-known and the schedule is allowed to change completely from period to period. Thus, precise adjustments to the demands of the market have a great potential for minimizing operating costs.
We propose a Branch-and-Cut approach to solve the airline schedule generation problem. To tighten the linear relaxation bound, we add cutting planes which adjust the number of aircraft and the spill of passengers to the demand on each itinerary.
For real-world problems from a large European charter airline we obtain solutions within a very few percent of optimality with running times in the order of minutes on a customary personal computer for most of the data sets.", } @TechReport{zpr99-350, author = "A. Erdmann and A. Nolte and J. Rathert and R. Schrader", institution = inf, title = "A Fast Solution Strategy for the Crew Pairing Problem", keywords = "Crew pairing, Dantzig-Wolfe decomposition, column generation, set partitioning", year = "1999", annote = "Airline crew scheduling is concerned with finding a minimum cost assignment of crews to flights while satisfying a number of rules like minimum rest time and maximal duty periods specified by union and governmental agreements. In this paper we describe a strategy for solving the Airline Crew Scheduling Problem approximately.
The problem is modeled as a set partitioning problem. We employ a dynamic column generation approach that adds columns to each node of the branch-and-bound tree and present computational results of our algorithm on problem instances of a major European airline. We investigate the influences of various strategies like branching rules and column selection on the solution time and quality. Additionally, our results are compared to the results of a local search implementation on the same instances, thus yielding one of the first direct comparisons of the two approaches.
The main point of this paper is that our algorithm is capable of solving large real world instances with a size typical for major carriers (up to 1400 flights) in the order of minutes on a usual PC. This opens up for the first time the possibility to integrate this approach in an interactive decision support environment.", } @TechReport{zpr99-349, author = "A. Erdmann and A. Nolte", institution = inf, title = "A Note on Constrained Shortest Path Algorithms in a Column Generation Framework", keywords = "Column generation, set partitioning, constrained shortest path algorithm, crew pairing", year = "1996", annote = "Column generation techniques embedded in a branch-and-bound tree have been widely used for transportation and scheduling problems in the past. In a number of applications constrained shortest path algorithms are used to dynamically generate new columns. Typically, the major part of the running time and the main memory requirement is consumed during the execution of the constrained shortest path subroutines.
We propose a progress dependent limitation on the number of labels on nodes and arcs, respectively, and prove the efficiency of this approach by presenting experimental results on real world crew pairing problems from a major German cargo airline.", } @InProceedings{zpr99-348a, author = "A. Nolte and R. Schrader", institution = mi, title = "Simulated Annealing and its Problems to color graphs", keywords = "Simulated Annealing, inhomogeneous Markov chain, convergence;", booktitle = "Algorithms - ESA '96, 5th Annual European Symposium", location = "Barcelona, Spain", editors = "J. Díaz and M. Serna", series = "Lecture Notes in Computer Science", volume = "1136", publisher = "Springer-Verlag", pages = "138--151", year = "1996", } @Article{zpr99-348, author = "A. Nolte and R. Schrader", institution = mi, title = "Simulated Annealing and its Problems to color graphs", crindex = "97k,15,zpr98-348.ps.gz", keywords = "Simulated Annealing, inhomogeneous Markov chain, convergence;", journal = "submitted to Combinatorics, Probability and Computing", annote = "Simulated Annealing is a very successful heuristic for various problems in combinatorial optimization. In this paper an application of Simulated Annealing to the 3-coloring problem is considered. In contrast to many good empirical results we will show for a certain class of graphs that the expected first hitting time of a proper coloring, given an arbitrary cooling scheme, is of exponential size.

These results are complementary to those in zpr99-347, where the convergence of Simulated Annealing to an optimal solution in exponential time is proved.", } @InProceedings{zpr99-347a, author = "A. Nolte and R. Schrader", institution = mi, title = "A Note on the Finite Time Behaviour of Simulated Annealing", booktitle = "Operations Research Proceedings", editor = "U. Zimmermann and U. Derigs and W. Gaul and R. M{\"o}hring and K.-P. Schuster", location = "Braunschweig, Germany", pages = "175--180", publisher = "Springer", year = "1996", keywords = "Simulated Annealing, inhomogeneous Markov chain, convergence;", } @Article{zpr99-347, author = "A. Nolte and R. Schrader", institution = mi, title = "A Note on the Finite Time Behaviour of Simulated Annealing", crindex = "89k,11,zpr98-347.ps.gz", keywords = "Simulated Annealing, inhomogeneous Markov chain, convergence;", journal = "accepted for publication: Mathematics of OR", annote = "Simulated Annealing has proven to be a very sucessful heuristic for various combinatorial optimization problems. It is a randomized algorithm that attempts to find the global optimum with high probability by local exchanges. In this paper we give a new proof of the convergence of Simulated Annealing by applying results about rapidly mixing Markov chains. With this proof technique it is possible to obtain better bounds for the finite time behaviour of Simulated Annealing than previously known.", } @Article{zpr99-346, author = "F. Castiglione and Francesco Castiglione", insitution = inf, title = "Estimating the Keratoconus Index from ultrasound images of the human cornea", booktitle = "Submitted to: IEEE Transactions on Medical Imaging", crindex = "223k,3,zpr99-346.ps.gz", keywords = "keratoconus, cornea, image analysis; 68U10", annote = "The keratoconus index (KI) is a valuable measure to make diagnosis of the keratoconus in human eyes. Using images from an ultrasound biomicroscope, we show a method to automatically compute the KI and, ultimately, to make diagnosis of the keratoconus.", } @Article{zpr99-345, author = "M. Bernaschi and F. Castiglione and S. Succi", insitution = inf, title = "A high performance simulator of the Immune Response", journal = "Future Generation Computer System", volume = "15", number = "3", pages = "333--342", year = "1999", publisher = "Elsevier Science", crindex = "42k,4,zpr99-345.ps.gz", keywords = "Immune System, Celada-Seiden model, parallel computing, population dynamics, cellular automata; 92D25,65Y05", annote = "The application of concepts and methods of statistical mechanics to biological problems is one of the most promising frontiers of computational physics. For instance Cellular Automata (CA), i.e. fully discrete dynamical systems evolving according to boolean laws, appear to be extremely well suited to the simulation of the immune system dynamics. A prominent example of immunological CA is represented by the Celada-Seiden automaton, that has proven capable of providing several new insights into the dynamics of the immune system response.
In the present paper we describe a parallel version of the Celada-Seiden automaton. Details on the parallel implementation as well as performance data on the IBM SP2 parallel platform are presented and commented on.", } @InProceedings{zpr99-344, author = "M. Bernaschi and F. Castiglione and P. Seiden and S. Succi", insitution = inf, title = "Learning Cascade in the immune system dynamics: a numerical simulation", booktitle = "Int. Conf.on Computational Physics (CCP98), Grenada Nov 1998", crindex = "92k,13,zpr99-344.ps.gz", keywords = "Information Entropy, Immune System, Celada-Seiden model, population dynamics, 92D25,65Y05", annote = "The idea of learning cascade, recently introduced to characterize the progressive evolution of the immune system response from low-affinity to high-affinity lymphocites, is explored by means of extensive computer simulations.", } @TechReport{zpr99-343, author = "W. Hochst{\"a}ttler and J. Nesetril", institution = mi, title = "A Note on MaxFlow-MinCut and Homomorphic Equivalence in Matroids", year = "1999", crindex = "36k,5,zpr99-343.ps.gz", keywords = "matroids, strong map, homomorphism, duality, Menger's theorem; 05B35, 05B40, 05C38, 05C70, 18B99, 90C27", annote = "This paper is considerably modified revision of 97-286 and contains several new results:

In this note we point out that the validity of the max-flow-min-cut theorem in a matroid port M is equivalent to the homomorphic equivalence of the dual port M* to a circuit in the category of matroid ports and strong port maps. As a consequence, restricting to the category of matroids with the strong integer MaxFlow-MinCut property, one has a linearly ordered set of equivalence classes and Menger's Theorem as the unique homomorphism duality.", } @TechReport{zpr99-342, author = "U. Blasum and W. Hochst{\"a}ttler and P. Oertel", insitution = mi, title = "Steiner-Diagrams", year = "1999", crindex = "53k,8,zpr93-342.ps.gz", keywords = "Steiner diagram, vehicle routing, Steiner arborescence, Steiner tree, min-cost flow, computational complexity, NP-completeness; 90B06, 05C38", annote = "In this report, we introduce and study the Steiner-diagram-problem. Given a digraph G=(V,A,w) with non-negative edge-weights and a set of demand edges B, the objective is to find an acyclic set of edges of minimal cost, whose transitive closure contains B. We will show that this problem is NP-complete in the general case and that it is polynomially solvable if the size of B is bounded by a constant.", } @Article{zpr98-341, author = "B. Randerath and I. Schiermeyer", insitution = inf, title = "Colouring Graphs with Prescribed Induced Cycle Lengths", journal = "Submitted to: Journal of Combinatorial Theory B", crindex = "94k,9,zpr98-341.ps.gz", keywords = "colouring, chromatic number, cycle lengths, induced subgraphs, graph algorithms; 05C15, 05C38, 05C75, 05C85", annote = "In this paper we study the chromatic number for graphs with two prescribed induced cycle lengths. It is due to Sumner that triangle-free and P5-free and triangle-free, P6-free and C6-free graphs are 3-colourable. A canonical extension of these graph classes is ${\cal{G}}^I(4,5)$, the class of all graphs whose induced cycle lengths are 4 or 5. Our main result states that all graphs of ${\cal{G}}^I(4,5)$ are 3-colourable. Moreover, we present polynomial time algorithms to 3-colour all triangle-free graphs G of this kind. Thus, every $G\in {\cal{G}}^I(n_1,n_2)$ with $n_1,n_2\geq 4$ is 3-colourable. Furthermore, we consider the related problem of finding a $\chi$-binding function for the class ${\cal G}^I(n_1,n_2)$.

An extended abstract of this paper appears in SODA `99.", } @Article{zpr98-340a, author = "S. P. Fekete and H. Meijer", insitution = mi, title = "On Minimum Stars, Minimum Steiner Stars, and Maximum Matchings", booktitle = "to appear in: Discrete and Computational Geometry", crindex = "129k,19,zpr98-340a.ps.gz", keywords = "Maximum matching, Weber problem, connected network, combinatorial optimization, geometric optimization, geometric inequalities, extremal properties, Euclidean norm, rectilinear norm, computational complexity; 51M16, 90C27", } @InProceedings{zpr98-340, author = "S. P. Fekete and H. Meijer", insitution = mi, title = "On Minimum Stars, Minimum Steiner Stars, and Maximum Matchings", booktitle = "Proceedings of the Fifteenth Annual Symposium on Computational Geometry, June 13-16, 1999, Miami Beach, Florida, USA", pages = "217--226", publisher = "ACM Press", year = "1999", crindex = "76k,10,zpr98-340.ps.gz", keywords = "Maximum matching, Weber problem, connected network, combinatorial optimization, geometric optimization, geometric inequalities, extremal properties, Euclidean norm, rectilinear norm, computational complexity; 51M16, 90C27", annote = "We discuss properties and values of maximum matchings and minimum median problems for finite point sets. In particular, we consider ``minimum stars'', which are defined by a center chosen from the given point set, such that the total geometric distance |St| to all the points in the set is minimized. If the center point is not required to be an element of the set (i.e., the center may be a Steiner point), we get a ``minimum Steiner star'', of total length |StSt|. As a consequence of triangle inequality, the total length max|Mat| of any maximum matching is a lower bound for the length min|StSt| of a minimum Steiner star, which makes this ratio interesting in the context of optimal communication networks. The ratio also appears as the duality gap in an integer programming formulation of a location problem by Tamir and Mitchell.
In this paper, we show that for an even set of points in the plane and Euclidean distances, the ratio min|StSt|/max|Mat| cannot exceed 2/sqrt{3}. This proves a conjecture of Suri, who gave an example where this bound is achieved. For the case of Euclidean distances in two and three dimensions, we also prove upper and lower bounds for the maximal value of the ratios min|St|/min|StSt| and min|St|/max|Mat|. We give tight upper bounds for the case where distances are measured according to the Manhattan metric: We show that in three-dimensional space, min|StSt|/max|Mat| is bounded by 3/2, while in two-dimensional space min|StSt|=max|Mat|, extending some independent observations by Tamir and Mitchell. Finally, we show that min|St|/min|StSt| has a tight bound of 3/2 in the two-dimensional case, and of 5/3 in the three-dimensional case.", } @Article{zpr98-339, author = "C. Gawron", institution = mi, title = "An Iterative Algorithm to Determine the Dynamic User Equilibrium in a Traffic Simulation Model", journal = "International Journal of Modern Physics C", volume = "9", number = "3", pages = "393--408", year = "1998", crindex = "769k,14,zpr98-338.ps.gz", keywords = "traffic simulation, dynamic traffic assignment, dynamic user equilibrium, Braess's Paradox; 90B20, 90A56, 90B22", annote = "An iterative algorithm to determine the dynamic user equilibrium with respect to link costs defined by a traffic simulation model is presented. Each driver's route choice is modelled by a discrete probability distribution which is used to select a route in the simulation. After each simulation run, the probability distribution is adapted to minimize the travel costs. Although the algorithm does not depend on the simulation model, a queuing model is used for performance reasons. The stability of the algorithm is analyzed for a simple example network. As an example application, a dynamic version of Braess's paradox is studied.", } @TechReport{zpr98-338, author = "C. Gawron and S. Krau{\ss} and P. Oertel and F. P{\"u}tsch and C. R{\"o}ssel and P. Wagner", institution = mi, title = "The PlanSim-Traffic simulation", year = "1998", crindex = "548k,27,zpr98-338.ps.gz", keywords = "traffic simulation;", annote = "This text documents the PlanSim-T micro-simulation which is intended to simulate a road network. PlanSim-T's main feature is the ability to play with different traffic flow models in their natural environment, i.e. networks of streets.

The main features of PlanSim-T are:

", } @Article{zpr98-337, author = "T. Fleiner and W. Hochst{\"a}ttler and M. Laurent and M. Loebl", institution = mi, title = "Cycle bases for lattices of matroids with no Fano dual minor and their one-element extensions", journal = "Journal of Combinatorial Theory B", volume = "77", number = "1", pages = "25--38", year = "1999", crindex = "65k,13,zpr98-337.ps.gz", keywords = "geometry of numbers, binary matroids, lattice basis; 05B40, 11H31, 52C17", annote = "In this paper we study the question of existence of a basis consisting only of cycles for the lattice Z(M) generated by the cycles of a binary matroid M. We show that, if M has no Fano dual minor, then any set of fundamental circuits can be completed to a cycle basis of Z(M); moreover, for any one-element extension M of such matroid M, any cycle basis for Z(M) can be completed to a cycle basis for Z(M).

This is a revised version of 96-249. The major change is a considerable simplification of the proof of Theorem 3.1 contributed by Tamas Fleiner which gives additional insight into the structure.", } @TechReport{zpr98-336, author = "J. Teich and S. P. Fekete and J. Schepers", insitution = mi, title = "Optimizing Dynamic Hardware Reconfigurations", crindex = "112k,12,zpr98-336.ps.gz", keywords = "Field-programmable gate arrays (FPGA's), hardware reconfiguration, packing, 3-dimensional geometry, exact algorithms, branch-and-bound, geometric optimization, interval graphs; 90C28, 68R99", annote = "With the advent of recent generations of Field Programmable Gate Arrays, it has become possible to use computing resources more efficiently by dynamically reconfiguring hardware (during run-time). This is achieved by reassigning computation modules or tasks to unused cells. For a given problem consisting of a set of tasks, possibly with partial order constraints, we consider problems such as finding the minimal area chip to accomplish the tasks within a given time limit. These problems turn out to be multi-dimensional packing problems. With the new notion of packing classes, we show how the search space may be significantly reduced, such that these problems can be solved exactly in an affordable amount of time for problems of technical interest using special branch-and-bound techniques. We validate the usefulness of our method by providing computational results.", } @InProceedings{zpr98-335, author = "E. Dahlhaus", insitution = inf, title = "Minimal Elimination Orderings for Planar Graphs", booktitle = "Algorithm Theory - SWAT'98, Proc. of 6th Scandinavian Workshop on Algorithm Theory", location = "Stockholm, Sweden", editor = "S. Arnborg and L. Ivansson", series = "Lecture Notes in Computer Science", volume = "1432", publisher = "Springer-Verlag", year = "1998", crindex = "113k,22,zpr98-335.ps.gz", keywords = "graph algorithms, planar graphs, chordal graphs, sparse Gauss elimination; 05C50, 65F50, 68R10", annote = "We prove that the problem to get an inclusion minimal elimination ordering can be solved in linear time for planar graphs. The basic structure of the linear time algorithm is as follows. We select a vertex r as maximum and get a first approximation of a minimal elimination ordering considering a vertex x as smaller than y if x has a larger distance than y from r. Using planarity, one can determine the fill-in edges joining two vertices of the same distance from r almost immediately. The algorithm determines an O(n)-representation of these fill-in edges. To determine the final fill-in ordering, we use similar techniques as in the general parallel minimal elimination algorithm of Elias Dahlhaus, Marek Karpinski [An Efficient Parallel Algorithm for the Minimal Elimination Ordering (MEO) of an Arbitrary Graph, Theoretical Computer Science 134, 493-528 (1994)].

An extended abstract of this paper appeared in SWAT '98.", } @TechReport{zpr98-334, author = "F. Brockners", insitution = mi, title = "{FEC} Supported Congestion Control in One to Many Reliable Multicast", crindex = "1746k,30,zpr98-334.ps.gz", keywords = "Congestion Control, Forward Error Correction, FEC, Reliable Multicast;", annote = "This paper describes the design of a new FEC fueled rate and congestion controller (RCR) which is targeted primarily at one to many reliable bulk multicast data transfer. The concept of RCR is validated by analytical and simulation results. The heuristic analysis is based on a new extended model for flows, which implement a congestion control algorithm similar to TCP. The main goal was to develop an algorithm which is TCP-friendly and competes with the control loop of TCP. Large delays in the control circuit, scaling issues and high packet loss probabilities are among the major challenges of a reliable multicast rate controller implementing TCP-fair congestion control. The controller presented in this paper shows that layered forward error correction (FEC) redundancy coding not only reduces the control- and retransmissions in reliable multicast environments using automatic repeat requests (ARQ) to trigger retransmissions but also helps a congestion controller to compete with TCP. FEC permits the receivers to tolerate losses in a way that they only need to signalize loss levels which are significant for them. This high-pass filtering of the loss signal reverts the disadvantage of reacting slowly to loss into an advantage in direct comparison to TCP. The greater responsiveness with respect to rate increment ensures that TCP always receives its share of the total available bandwidth. Simulations and analytical analysis for multicast as well as unicast setups show that already a very moderate level (some \%) of redundancy suffices to strengthen a connection suffering from long delays and high loss probabilities.", } @Article{zpr98-333, author = "A. Barvinok and S. P. Fekete and D. S. Johnson and A. Tamir and G. J. Woeginger and D. Woodroofe", insitution = mi, title = "The Maximum Traveling Salesman Problem", journal = "submitted to: Journal of Algorithms", keywords = "Traveling Salesman Problem, combinatorial optimization, geometric optimization, Euclidean norm, polyhedral norm, computational complexity; 90C27", annote = "In this paper, we present a number of results on the Maximum TSP, i.e., the problem of finding a traveling salesman tour of maximum length. In particular, we show that the problem can be solved in polynomial time, provided that distances are computed according to a polyhedral norm in Rd, for some fixed d. The most natural case of this class of problems arises for rectilinear distances in the plane Rp, where the unit ball is a square. We also present a simple algorithm with O(n) running time for computing the length of a longest tour for a set of points in the plane with rectilinear distances. In addition, our approach gives a simple characterization of all optimal solutions. These results give a good idea what makes the (polyhedral) max TSP so much easier than its minimization counterpart.
The results on simplicity are complemented by a proof that the Maximum TSP under Euclidean distances in Rd for any fixed d >= 3 is NP-hard, shedding new light on the well-studied difficulties of Euclidean distances.", } @TechReport{zpr98-332, author = "O. Bastert and S. P. Fekete", insitution = mi, title = "Geometric Wire Routing", keywords = "Geometric optimization, VLSI design, complexity, lower bounds; 68Q35, 68U05, 90C28", annote = "We consider the problem of connecting n pairs of points in the plane by pairwise disjoint geometric paths (``wires''). This problem is closely related to geometric aspects of chip layout; the question of the existence of a set of pairwise disjoint connections has been studied widely. In a purely geometric setting, there always is a set of disjoint wires, so the main issue is to optimize the layout. We consider several objective functions involving the length as well as the number of bends of the wires.
We present techniques for showing NP-hardness of this type of geometric problem.", } @Article{zpr98-331, author = "S. P. Fekete and W. R. Pulleyblank", insitution = mi, title = "A note on the Traveling Preacher Problem", journal = "submitted to: Operations Research Letters", crindex = "37k,5,zpr98-331.ps.gz", keywords = "Traveling Salesman Problem, combinatorial optimization, cooperative games, core allocation, polynomial algorithm, computational complexity; 90C27, 90D12", annote = "In this paper, we consider a problem of cost allocations for shortest roundtrips. Given a weighted graph G=(V,E), we are to find a subset S of V with a maximum weight core element for the Traveling Preacher game, i.e., a subset S of V with a maximum cost allocation x(S) to the vertices, such that there is no nontrivial subset S' of S of vertices with a total cost allocation x(S') exceeding the cost of a Traveling Salesman tour visiting the vertices in the subset S. This game can be considered as a variant of the so-called Traveling Saleman game, with the difference that there is no specified central root node for the salesman. We show that this ``Traveling Preacher Problem'' can be solved in polynomial time, showing that the difficulty of finding a core allocation for a combinatorial optimization problem may be caused by the existence of a special depot node, rather than being a consequence of the hardness of the optimization problem itself.", } @TechReport{zpr98-330, author = "S. P. Fekete and H. Meijer", insitution = mi, title = "On Maximum Matchings and Minimum Steiner Stars", crindex = "62k,11,zpr98-330.ps.gz", keywords = "Maximum matching, Weber problem, connected network, combinatorial optimization, geometric optimization, geometric inequalities, extremal properties, Euclidean norm, rectilinear norm, computational complexity; 51M16, 90C27", annote = "We discuss properties and values of maximum matchings and minimum median problems for finite point sets. In particular, we consider ``minimum stars'', which are defined by a center chosen from the given point set, such that the total geometric distance to all the points in the set is minimized. If the center point is not required to be an element of the set (i.e., the center may be a Steiner point), we get a ``minimum Steiner star'', of total length |StSt|. As a consequence of triangle inequality, the total length max|Mat| of any maximum matching is a lower bound for the length min|StSt| of a minimum Steiner star, which makes this ratio interesting in the context of optimal communication networks. The ratio also appears as the duality gap in an integer programming formulation of a location problem by Tamir and Mitchell.
In this paper, we show that for an even set of points in the plane and Euclidean distances, the ratio min|StSt|/max|Mat| cannot exceed 2/sqrt{3}. This proves a conjecture of Suri, who gave an example where this bound is achieved. We also give results for the case where distances are measured according to the Manhattan metric, extending some observations by Tamir and Mitchell.", } @InProceedings{zpr98-329, author = "S. P. Fekete", insitution = mi, title = "Simplicity and Hardness of the Maximum Traveling Salesman Problem under Geometric Distances", booktitle = "Proceedings of the Tenth Annual ACM/SIAM Symposium on Discrete Algorithms (SODA'99)", pages = "337--345", crindex = "80k,15,zpr98-329.ps.gz", keywords = "Traveling Salesman Problem, combinatorial optimization, geometric optimization, Euclidean norm, polyhedral norm, computational complexity; 90C27", annote = "Recently, Barvinok, Johnson, Woeginger, and Woodroofe have shown that the Maximum TSP, i.e., the problem of finding a traveling salesman tour of maximum length, can be solved in polynomial time, provided that distances are computed according to a polyhedral norm in Rd, for some fixed d. The most natural case of this class of problems arises for rectilinear distances in the plane Rp, where the unit ball is a square. With the help of some additional improvements by Tamir, the method by Barvinok et al. yields an O(n2log n) algorithm for this case by making elegant use of geometry, graph theory, and optimization, including some rather powerful tools.
In this paper, we present a simple algorithm with O(n) running time for computing the length of a longest tour for a set of points in the plane with rectilinear distances. The algorithm does not use any indirect addressing, so its running time remains valid even in comparison based models in which sorting requires Omega(n log n) time, which implies the same lower bound on verifying a Hamiltonian cycle. In addition, our approach gives a simple characterization of all optimal solutions. These results give a good idea what makes the (polyhedral) max TSP so much easier than its minimization counterpart.
Resolving the complexity status of the max TSP for Euclidean distances in spaces of fixed dimension has been stated by Barvinok et al. as a main open problem. In this paper, the results on simplicity are complemented by a proof that the Maximum TSP under Euclidean distances in Rd for any fixed d >= 3 is NP-hard, shedding new light on the well-studied difficulties of Euclidean distances. In addition, our result implies NP-hardness of the Maximum TSP under polyhedral norms if the number k of facets of the unit ball is not fixed. As a corollary, we get NP-hardness of the Maximum Scatter TSP for geometric instances, where the objective is to find a tour that maximizes the shortest edge. This resolves a conjecture by Arkin, Chiang, Mitchell, Skiena, and Yang in the affirmative.", } @Article{zpr98-328, author = "R. Schrader and A. S. Schulz and G. Wambach", insitution = inf, title = "Base polytopes of series-parallel posets: Linear description and optimization", journal = "Mathematical Programming", volume = "82", number = "1-2", series = "B", pages = "159--173", year = "1998", publisher = "Elsevier Science B.V.", keywords = "polyhedral combinatorics, series-parallel posets, base polytopes, supermodular functions, greedy algorithm, integer programming;", annote = "We define the base polytope B(P,g) of a partially ordered set P and a supermodular function g on the ideals of P as the convex hull of the incidence vectors of all linear extensions of P. This new class of polytopes contains, among others, the base polytopes of supermodular systems and permutahedra as special cases. After introducing the notion of compatibility for g, we give a complete linear description of B(P,g) for series--parallel posets and compatible functions g. In addition, we describe a greedy-type procedure which exhibits Sidney's job sequencing algorithm to minimize the total weighted completion time as a natural extension of the matroidal greedy algorithm from sets to posets.

Full text as PDF.", } @Article{zpr98-327, author = "T. Fleiner and V. Kaibel and G. Rote", institution = inf, title = "Upper Bounds on the Maximal Number of Facets of 0/1-Polytopes", journal = "to appear in: European Journal of Combinatorics", year = "1998", crindex = "95k,12,zpr98-327.ps.gz", keywords = "0/1-Polytopes, Facets; 52B12, 52B20", annote = "We prove two new upper bounds on the number of facets that a d-dimensional 0/1-polytope can have. The first one is 2(d-1)!+2(d-1) (which is the best one currently known for small dimensions), while the second one of O((d-2)!) is the best known bound for large dimensions.", } @Article{zpr98-326, author = "V. Kaibel and M. Wolff", institution = inf, title = "Simple 0/1-Polytopes", journal = "accepted for publication: European Journal of Combinatorics", year = "1998", crindex = "70k,6,zpr98-326.ps.gz", keywords = "0/1-Polytopes, Simple Polytopes, 0/1-Simplices; 52B12, 52B20", annote = "For general polytopes, it has turned out that with respect to many questions it suffices to consider only the simple polytopes, i.e., d-dimensional polytopes where every vertex is contained in only d facets. In this paper, we show that the situation is very different within the class of 0/1-polytopes, since every simple 0/1-polytope is the (cartesian) product of some 0/1-simplices (which proves a conjecture of Ziegler), and thus, the restriction to simple 0/1-polytopes leaves only a very small class of objects with a rather trivial structure.", } @TechReport{zpr98-325, author = "E. Dahlhaus", institution = inf, title = "Linear Time Algorithm to Recognize Clustered Planar Graphs and its Parallelization", year = "1998", crindex = "186k,18,zpr98-325.ps.gz", keywords = "parallel algorithms, graph algorithms, hierarchical clustering, planar graphs, graph drawing; 68R10, 68Q22, 68Q25, 68Q35", annote = "We develop a linear time algorithm for the following problem: Given a graph G and a hierarchical clustering of the vertices, such that all clusters induce connected subgraphs, determine whether G can be embedded into the plane, such that no cluster has a hole.
This is an improvement to the quadratic time algorithm of Q.W. Feng et al. [Planarity for Clustered Graphs, ESA ´96, Springer LNCS 979, pp. 213-226] and the algorithm of Lengauer [Hierarchical Planarity Testing Algorithm, Journal of the ACM 36 (1989), pp. 474-509].", } @InProceedings{zpr98-325a, author = "E. Dahlhaus", institution = inf, title = "Linear Time Algorithm to Recognize Clustered Planar Graphs and its Parallelization (Extended Abstract)", booktitle = "LATIN '98, 3rd Latin American symposium on theoretical informatics, Campinas, Brazil, April 20--24, 1998.", editor = "C. L. Lucchesi", series = "Lecture Notes in Computer Science", volume = "1380", pages = "239--248", year = "1998", } @TechReport{zpr98-324, author = "E. Dahlhaus", institution = inf, title = "Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition", year = "1998", crindex = "158k,35,zpr98-324.ps.gz", keywords = "parallel algorithms, graph algorithms, split decomposition, hierarchical clustering, single linkage; 68R10, 68Q22, 68Q25", annote = "We present efficient (parallel) algorithms for two hierarchical clustering heuristics. We point out that these heuristics can also be applied to solve some algorithmic problems in graphs. This includes split decomposition. We show that efficient parallel split decomposition induces an efficient parallel parity graph recognition algorithm. This is a consequence of the result of Cicerone and di Stephano that parity graphs are exactly those graphs that can be split decomposed into cliques and bipartite graphs.", } @TechReport{zpr98-323, author = "N. Ascheuer and M. J{\"u}nger and G. Reinelt", institution = inf, title = "A Branch-and-Cut Algorithm for the Asymmetric Hamiltonian Path Problem with Precedence Constraints", booktitle = "to appear in: Computational Optimization and Applications", year = "1998", crindex = "146k,23,zpr98-323.ps.gz", keywords = "asymmetric traveling salesman problem, precedence constraints, branch-and-cut;", annote = "In this article we consider a variant of the classical asymmetric traveling salesman problem, namely the asymmetric Hamiltonian path problem in which precedence constraints require that certain nodes must precede certain other nodes in any feasible directed Hamiltonian path. This problem occurs as a basic model in scheduling and routing and has a wide range of applications varying from helicopter routing (Timlin 1989), sequencing in flexible manufacturing (Ascheuer, Escudero, Gr{\"o}tschel, Stoer, 1990; Ascheuer, Escudero, Gr{\"o}tschel, Stoer, 1993), to stacker crane routing in an automatic storage system (Ascheuer, 1995).
We give an integer programming model and summarize known classes of valid inequalities. We describe in detail the implementation of a branch-and-cut algorithm and give computational results on real world instances and benchmark problems from TSPLIB. The results we achieve indicate that our implementation outperforms other implementations found in the literature. Real world instances with more than 200 nodes can be solved to optimality within a few minutes of CPU-time.
As a side product we obtain a branch-and-cut algorithm for the ATSP. All instances in TSPLIB can be solved to optimality in a reasonable amount of computation time.", } @TechReport{zpr98-322, author = "M. J{\"u}nger and S. Thienel", institution = inf, title = "The {ABACUS} System for Branch-and-Cut and Prices Algorithms in Integer Programming and Combinatorial Optimization", journal = "to appear in: Software - Practice and Experience", year = "1998", annote = "The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an object-oriented software framework for branch-and-cut-and-price algorithms for the solution of mixed integer and combinatorial optimization problems. This paper discusses some difficulties in the implementation of branch-and-cut-and-price algorithms for combinatorial optimization problems and shows how they are managed by ABACUS.", } @InProceedings{zpr98-321, author = "M. J{\"u}nger and S. Leipert and P. Mutzel", institution = inf, title = "Level Planarity Testing in Linear Time (Extended Abstract)", booktitle = "Proc. 6th International Symposium on Graph Drawing '98", location = "Montreal, Canada", editor = "S. H. Whitesides", series = "Lecture Notes in Computer Science", volume = "1547", publisher = "Springer-Verlag", year = "1999", crindex = "101k,10,zpr98-321.ps.gz", keywords = "level planarity, PQ-trees; 05C85, 68R10, 90C35", annote = "In a leveled directed acyclic graph G = (V,E) the vertex set V is partitioned into k <= |V| levels V1,V2,...,Vk such that for each edge (u,v) in E with u in Vi and v in Vj we have i < j. The level planarity testing problem is to decide if G can be drawn in the plane such that for each level Vi, all v in Vi are drawn on the line li = {(x,k-i) | x in R}, the edges are drawn monotone with respect to the vertical direction, and no edges intersect except at their end vertices. If G has a single source, the test can be performed in O(|V|) time by an algorithm of Di Battista and Nardelli [Hierarchies and planarity theory. IEEE Trans. Systems Man Cybernet. 18 (1988), no. 6, 1035--1046] that uses the PQ-tree data structure introduced by Booth and Lueker [Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. System Sci. 13 (1976), no. 3, 335--379].
PQ-trees have also been proposed by Heath and Pemmaraju (1996a,1996b) to test level planarity of leveled directed acyclic graphs with several sources and sinks. It has been shown in J{\"u}nger, Leipert and Mutzel (1997) that this algorithm is not correct in the sense that it does not state correctly level planarity of every level planar graph. In this paper, we present a correct linear time level planarity testing algorithm that is based on two main new techniques that replace the incorrect crucial parts of the algorithm of Heath and Pemmaraju (1996a,1996b).", } @Article{zpr98-320, author = "M. J{\"u}nger and S. Leipert and P. Mutzel", institution = inf, title = "A Note on Computing a Maximal Planar Subgraph using {PQ}-Trees", journal = "IEEE Transactions on COMPUTER-AIDED DESIGN of Integrated Circuits and Systems", volume = "17", number = "7", year = "1998", crindex = "102k,10,zpr98-320.ps.gz", keywords = "PQ-trees,maxumal planar subgraphs,planarization; 05C85, 68R10,90C35", annote = "The problem of computing a maximal planar subgraph of a non planar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of PQ-trees. The latest attempt has been reported by Jayakumar et al. (1989).
In this paper we show that the algorithm presented by Jayakumar et al. is not correct. We show that it does not necessarily compute a maximal planar subgraph and we note that the same holds for a modified version of the algorithm presented by Kant (1992). Our conclusions most likely suggest not to use PQ-trees at all for this specific problem.", } @PhdThesis{zpr98-319, author = "S. Krau{\ss}", institution = mi, title = "Microscopic Modeling of Traffic Flow: Investigation of Collision Free Vehicle Dynamics", year = "1998", pages = "116", crindex = "1399k,119,zpr98-319.ps.gz", keywords = "statistical processes, interacting random processes, statistical mechanics type modells, highway traffic; 60K30, 60K35, 90B20", annote = "The continuous growth of road traffic volumes leads to significant environmental and economical problems. For this reason there have been efforts for more than four decades to understand the dynamics of traffic flow in order to find ways to optimize traffic with respect to a reduction of environmental impacts and economical losses due to congestion.
In this work a microscopic model of traffic flow is proposed that adds to the understanding of the different types of congestion that are found in traffic flow. The main assumption the model is based on is the fact that in general vehicles move without colliding. From this property of vehicle motion a model can be derived that shows a rich dynamics and proves to be in good agreement with empirical data.
The model is mainly characterized by the parameters describing typical acceleration and deceleration capabilities of the vehicles. It closely resembles other well-known models for certain choices of these parameters. By varying acceleration and deceleration capabilities a thorough understanding of the dynamics of the model and the previously known special cases is gained.", } @TechReport{zpr98-318, author = "B. G{\"a}rtner and V. Kaibel", institution = inf, title = "Abstract Objective Function Graphs on the 3-cube
{A} Classification by Realizability", year = "1998", crindex = "78k,12,zpr98-318.ps.gz", keywords = "linear programming, 3-Cube, abstract objective function, realization; 52B10, 52B12, 90C05", annote = "We call an orientation of the graph of a simple polytope P an abstract objective function (AOF) graph if it satisfies two conditions that make the simplex algorithm (e.g. with the Random-Facet pivot rule of Kalai and Matousek, Sharir, and Welzl) work: it has to be acyclic and it has to induce a unique sink in every subgraph that corresponds to a face of the polytope. For the graph of the 3-dimensional cube we investigate the question which among all possible AOF graphs are realizable in the sense that they are induced by some linear program (with a polytope of feasible solutions that is combinatorially a 3-dimensional cube). It turns out that (up to isomorphism) precisely two AOF graphs are not realizable.", } @TechReport{zpr98-317, author = "S. P. Fekete", institution = mi, title = "Finding maximum length tours under Euclidean norms", year = "1998", crindex = "39k,5,zpr98-317.ps.gz", keywords = "Traveling Salesman Problem, combinatorial optimization, geometric optimization, Euclidean norm, polyhedral norm, computational complexity; 90C27", annote = "Recently, Barvinok, Johnson, Woeginger, and Woodroofe have shown that the Maximum TSP, i.e., the problem of finding a traveling salesman tour of maximum length, can be solved in polynomial time, provided that distances are computed according to a polyhedral norm in Rd, for some fixed d. They stated as an open problem to resolve the complexity of finding a maximum length tour under Euclidean distances in a space of fixed dimension.
In this paper it is shown that the Maximum TSP under Euclidean distances in Rd for any fixed d > 2 is NP-hard, shedding new light on the well-studied difficulties of Euclidean distances. In addition, our result implies NP-hardness of the Maximum TSP under polyhedral norms if the number k of facets of the unit ball is not fixed, and NP-hardness of the Maximum Scatter TSP for geometric instances, where the objective is to find a tour that maximizes the shortest edge.", } @InProceedings{zpr98-316, author = "V. Kaibel", institution = inf, title = "Polyhedral Combinatorics of Quadratic Assignment Problems with Less Objects than Locations (Full Version)", booktitle = "Integer Programming and Combinatorial Optimization, Proc. 6th International IPCO Conference", location = "Houston, Texas", month = jun, year = "1998", editor = "R. E. Bixby and E. A. Boyd and R. Z. Ríos-Mercado", pages = "409--422", series = "Lecture Notes in Computer Science", volume = "1412", publisher = "Springer-Verlag", annote = "(This is the version for the Proceedings of the IPCO 98 conference. It is enriched by some proofs that have been left out in the extended abstract. A journal version with even more proofs will maybe be prepared as well.)
For the classical quadratic assignment problem (QAP) that requires n objects to be assigned to n locations (the n×n-case), polyhedral studies have been started in the very recent years by several authors. In this paper, we investigate the variant of the QAP, where the number of locations may exceed the number of objects (the m×n-case). It turns out that one can obtain structural results on the m×n-polytopes by exploiting knowledge on the n×n-case, since the first ones are certain projections of the latter ones. Besides answering the basic questions for the affine hulls, the dimensions, and the trivial facets of the m×n-polytopes, we present a large class of facet defining inequalities. Employed into a cutting plane procedure, these polyhedral results enable us to compute optimal solutions for some hard instances from the QAPLIB for the first time without using branch-and-bound. Moreover, we can calculate for several yet unsolved instances significantly improved lower bounds.", } @InProceedings{zpr98-315, author = "W. Hochst{\"a}ttler and M. Loebl", institution = mi, title = "Bases of Cocycle Lattices and Submatrices of a Hadamard Matrix", booktitle = "Contemporary Trends in Discrete Mathematics: From DIMACS and DIMATIA to the Future", series = "DIMACS Series in Discrete Mathematics and Theoretical Computer Science", volume = "49", editor = "R. L. Graham and J. Kratochvíl and J. Nesetril and F. S. Roberts", publisher = "AMS", year = "1999", crindex = "58k,14,zpr98-315.ps.gz", keywords = "geometry of numbers, binary matroids, lattice basis, Hadamard matrix; 05B40, 11H31, 52C17", annote = "We study the lattice lat(M) of cocycles of a binary matroid M. By an isomorphism we show that such lattices are equivalent to lattices generated by the columns of proper submatrices of Sylvester matrices of full row length. As an application we show that the cocycle lattice of a recursively defined class of matroids, including all binary matroids of rank four, always has a basis consisting of cocycles.", } @PhdThesis{zpr98-314, author = "M. Rickert", institution = mi, title = "Traffic Simulation on Distributed Memory Computers", year = "1997", crindex = "1684k,158,zpr98-314.ps.gz", keywords = "traffic simulation, parallel computation, cellular automata, relaxation of complex systems, vehicle routing, shortest path; 68Q22, 65B99, 68U20, 93E30, 90A58, 90B20, 60K30", annote = "We investigate a cellular automaton model for a simple traffic simulation. The simulation is used to generate realistic travel time feedback in an iterative process to relaxate a set of routes for a medium-sized test street network. We compare several parameter combinations influencing the relaxation process. Relaxed sets of routes are used to perform and compare simple 'on-line' re-routing approaches. The dissertation contains a chapter on the parallel implementation of the micro-simulation.", } @Article{zpr98-313a, author = "S. P. Fekete and J. Kremer", institution = mi, title = "Tree Spanners in Planar Graphs", journal = "invited to: Discrete Applied Mathematics", year = "1998", crindex = "108k,20,zpr98-313a.ps.gz", keywords = "graph spanners, planar graphs, distance in graphs, subgraphs, trees, complexity, polynomial algorithms; 05C12, 05C05", annote = "A tree t-spanner of a graph G is a spanning subtree H of G in which the distance between every pair of vertices is at most t times their distance in G. Spanner problems have received some attention, mostly in the context of communication networks. It is known that for general unweighted graphs, the existence of a tree 2-spanner can be decided in polynomial time, while it is NP-hard to decide whether a tree 4-spanner exists; the case t=3 is open, but has been conjectured to be hard.
In this paper, we consider tree spanners in planar graphs. We show that even for planar graphs, it is NP-hard to determine the minimum t for which a tree t-spanner exists. On the other hand, we prove that it can be decided in polynomial time whether a planar graph has a tree t-spanner for t=3, and we give a polynomial algorithm for determining the minimum t for planar graphs with bounded face lengths.", } @InProceedings{zpr98-313, author = "S. P. Fekete and J. Kremer", institution = mi, title = "Tree Spanners in Planar Graphs", booktitle = "Short version in: Graph-Theoretic Concepts in Computer Science, Proc. 24th International Workshop, WG'98", editors = "J. Hromkovic and O. Sykora", series = "Lecture Notes in Computer Science", location = "Smolenice Castle, Slovak Republic", volume = "1517", pages = "298--309", publisher = "Springer-Verlag", year = "1998", crindex = "72k,12,zpr98-313.ps.gz", keywords = "graph spanners, planar graphs, distance in graphs, subgraphs, trees, complexity, polynomial algorithms; 05C12, 05C05", annote = "A tree t-spanner of a graph G is a spanning subtree H of G in which the distance between every pair of vertices is at most t times their distance in G. Spanner problems have received some attention, mostly in the context of communication networks. It is known that for general unweighted graphs, the existence of a tree 2-spanner can be decided in polynomial time, while it is NP-hard to decide whether a tree 4-spanner exists; the case t=3 is open, but has been conjectured to be hard.
In this paper, we consider tree spanners in planar graphs. We show that even for planar graphs, it is NP-hard to determine the minimum t for which a tree t-spanner exists. On the other hand, we prove that it can be decided in polynomial time whether a planar graph has a tree t-spanner for t=3, and we give a polynomial algorithm for determining the minimum t for planar graphs with bounded face lengths.", } @Misc{zpr97-312, author = "S. P. Fekete", institution = mi, title = "Geometric Ideas for Graph Representation and for Cooperative Game Theory", year = "1997", crindex = "371k,54,zpr97-312.ps.gz", keywords = "Graph representation, visibility, graph drawing, 3-dimensional geometry, complexity, NP-hardness, logic engine, cooperative game, core, cost allocation, tax, traveling salesman problem, traveling preacher, Held-Karp bound, spanning tree, X3C, nucleolus, nucleon, matching; 05C10, 05C75, 68R05, 68R10, 90C27, 90D12", annote = "This thesis describes context and contents of six papers that use geometric ideas in graph representation, and in cooperative game theory.
The first three articles (available as 95-207, 96-224, 97-273) deal with visibility representations of graphs by objects in three-dimensional space. We give a variety of upper and lower bounds on the sizes of graphs that can be represented, as well as a general technique for proving hardness of non-rigid geometric graph representations.
In cooperative game theory (see 93-137, 94-166 and 94-178) we study cost allocation and savings distribution for several combinatorial optimization games. In particular, we deal with Traveling Salesman games, Minimum Spanning Tree games, and Matching games. We describe solution concepts that involve geometric ideas, partly by the geometry behind the allocation rules, partly by the structure of related polyhedra.", } @PhdThesis{zpr97-311, author = "M. Wottawa", institution = mi, title = "Struktur und algorithmische Behandlung von praxisorientierten dreidimensionalen Packungsproblemen", year = "1996", crindex = "404k,150,zpr97-311.ps.gz", keywords = "packing, bin packing, 3-dimensional packing; 05C90, 90B06, 90C27, 90C28, 90C35", annote = "Fast jedes Kind besitzt in seiner Spielzeugsammlung in irgendeiner Form einen Satz Baukl{\"o}tze, mit dem es au{\ss}er dem Bauen von unterschiedlichen Figuren auch noch eine weitere Fertigkeit erlernt: Das Packen der Baukl{\"o}tze in eine f{\"u}r diese bereitstehende Kiste. Die dabei angewendeten `Verfahren' wie Backtracking oder Sortieren nach der Gr{\"o}{\ss}e sind uns somit von fr{\"u}hester Kindheit an vertraut, auch wenn wir sie nie als solche erkannt und benannt haben. Prinzipiell ist das zugrunde liegende mathematische Problem aber schon in seiner eindimensionalen Version NP-schwer und geh{\"o}rt somit zu den schwierigen Problemen. Sollen Computer zur L{\"o}sung eines dreidimensionalen Packungsproblems eingesetzt werden, so sind dazu Algorithmen notwendig, die die dem menschlichen Gehirn eigene Assoziationsf{\"a}higkeit durch geeignete Regeln bez{\"u}glich der Struktur der erzeugten Muster ersetzen.
In der Praxis kommen Packungsprobleme vor allem im Logistikbereich vor. Neben den dort auftretenden dreidimensionalen Problemen des Beladens von Frachtcontainern, Lastwagen oder Kommissionierpaletten haben aber auch vornehmlich zweidimensionale Zuschnittprobleme der Stahl-, Holz- und Glasindustrie eine gro{\ss}e Bedeutung. Dar{\"u}berhinaus werden in der Literatur auch die folgenden Anwendungen als Packungsprobleme modelliert:


Eine bessere Packung erm{\"o}glicht dabei in allen diesen Bereichen gro{\ss}e Kosteneinsparungen. Durch die zunehmende Verbreitung der Datenverarbeitung in der Auftragsabwicklung von Speditionen und Luftfracht-Gesellschaften haben diese inzwischen auch die notwendigen Informationen {\"u}ber das zu verschickende Frachtgut, so da{\ss} der Einsatz von EDV-gest{\"u}tzten Packungsverfahren auch technisch m{\"o}glich wird.
Ein- und zweidimensionale Packungsprobleme sind schon lange Gegenstand der Forschung und werden auch in einigen Bereichen der Industrie schon praktisch umgesetzt. Dagegen existieren f{\"u}r dreidimensionale Probleme erst sehr wenige Algorithmen, obwohl die praktischen Problemstellungen der Logistik in fast allen F{\"a}llen dreidimensional sind. In dieser Arbeit werden wir die wichtigste Variante der Packungsprobleme untersuchen, bei der sowohl die zu beladenden als auch die zu verladenden Objekte quaderf{\"o}rmig sind.
Im ersten Kapitel geben wir zun{\"a}chst einen {\"U}berblick {\"u}ber die in der Praxis und der Literatur behandelten Packungsprobleme und f{\"u}hren eine neue Klassifizierung f{\"u}r die in dieser Arbeit betrachteten orthogonalen Packungsprobleme ein, die sowohl der Vereinfachung der Notation dient, als auch eine effiziente Klassifizierung bestehender Algorithmen erm{\"o}glicht. Weiterhin werden die wichtigsten Heuristiken vorgestellt, f{\"u}r deren L{\"o}sungen G{\"u}teschranken bekannt sind.
Im zweiten Kapitel werden m{\"o}gliche Darstellungen von Packmustern diskutiert. Dabei wird besonderes Augenmerk auf die Datenstrukturen des Ber{\"u}hrgraphen und des Sichtbarkeitsgraphen gelegt, da diese neben den notwendigen Informationen {\"u}ber die Plazierung der Kisten auch umfangreiche Informationen {\"u}ber die Nachbarschaftsstruktur jeder Kiste des Packmusters enthalten, und somit besonders geeignet f{\"u}r den praktischen Einsatz sind. F{\"u}r die Ber{\"u}hrgraphen k{\"o}nnen wir eine Charakterisierung aller Graphen angeben, f{\"u}r die es eine Darstellung als Packmuster gibt.
Die beiden folgenden Kapitel behandeln zwei sehr einfach strukturierte Probleme, deren Komplexit{\"a}tsstatus unbekannt ist. Dies ist zum einen das Packen m{\"o}glichst vieler gleichgro{\ss}er Quadrate in ein einfach zusammenh{\"a}ngendes Polygon und zum anderen das Packen m{\"o}glichst vieler gleichgro{\ss}er Rechtecke in ein gr{\"o}{\ss}eres Rechteck (`Pallet Loading'). Wir beschreiben strukturelle und algorithmische Ans{\"a}tze f{\"u}r diese beiden Probleme. Beim Packen von Polygonen kann die Struktur des Originalproblems erheblich reduziert werden. Beim Pallet-Loading-Problem k{\"o}nnen wir f{\"u}r drei Klassen von Probleminstanzen alle optimalen Packmuster angeben und haben somit erste Informationen {\"u}ber die Komplexit{\"a}t der Struktur der optimalen Packmuster gewonnen. F{\"u}r die dreidimensionale Variante des Pallet Loadings entwickeln wir ein neues heuristisches Verfahren.
Kapitel vier besch{\"a}ftigt sich mit Verfahren zur L{\"o}sung von ein- und zweidimensionalen Problemen. Insbesondere wird eine Fallstudie zum Packen von Badewannen und Duschwannen vorgestellt, die f{\"u}r einen Industriepartner durchgef{\"u}hrt wurde, und die sich inzwischen im praktischen Einsatz befindet.
Die letzten beiden Kapitel behandeln Verfahren zur L{\"o}sung von dreidimensionalen Packungsproblemen. In Kapitel sechs stellen wir mit dem Teilfolgen-Verfahren einen Algorithmus vor, der auf einem neuen Ansatz basiert, bei dem das Problem bez{\"u}glich zweier Dimensionen durch effiziente zweidimensionale Verfahren gepackt wird, w{\"a}hrend durch eine geschickte Auswahl der an diese {\"u}bergebenen Kisten auch die dritte Dimension optimiert wird.
Im siebten Kapitel wird die in Kapitel 2 vorgestellte Datenstruktur des Sichtbarkeitsgraphen benutzt, um einen effizienten Verbesserungsalgorithmus zu erstellen.", } @Article{zpr97-310, author = "M. Rickert and K. Nagel", institution = mi, title = "Experiences with a simplified microsimulation for the Dallas/Fort Worth area", journal = "International Journal of Modern Physics C", volume = "8", number = "3", pages = "483--503", year = "1997", crindex = "208,21,zpr97-310.ps.gz", keywords = "Statistical Processes: Applications, Flows in Networks (probabilistic), Highway Traffic, Cellular Automata, Route Planning; 60K30, 90B15, 90B20", annote = "We describe a simple framework for microsimulation of city traffic. A medium sized excerpt of Dallas was used to examine different levels of simulation fidelity of a cellular automaton method for the traffic flow simulation and a simple intersection model. We point out problems arising with the granular structure of the underlying rules of motion.", } @InProceedings{zpr97-309, author = "M. Rickert and P. Wagner and C. Gawron", institution = mi, title = "Real-time Simulation of the German Autobahn Network", booktitle = "Proc. of the 4th Workshop on Parallel Systems and Algorithms (PASA '96)", year = "1997", publisher = "World Scientific Publishing Co.", crindex = "105k,14,zpr97-309.ps.gz", keywords = "Statistical Processes: Applications, Flows in Networks (probabilistic), Highway Traffic, Parallel and distributed algorithms, Cellular Automata; 60K30, 90B15, 90B20, 68Q22", annote = "This work is part of our ongoing effort to design and implement a traffic simulation application capable of handling realistic problem sizes in multiple real-time. A 16-CPU SGI Power Challenger offers real-time for the whole German Autobahn network. On a workstation cluster we have reached multiple real-time for the Autobahn network of the state Nordrhein-Westfalen. In this paper we present the parallel architecture and techniques used in our implementation. We also give an upper-bound estimate for the scaling behavior of this type of simulation.", } @Article{zpr97-308, author = "M. Rickert and P. Wagner", institution = mi, title = "Parallel Real-time Implementation of Large-scale, Route-plan-driven Traffic Simulation", journal = "International Journal of Modern Physics C", volume = "7", number = "2", pages = "133--153", year = "1996", crindex = "115,19,zpr97-308.ps.gz", keywords = "Statistical Processes: Applications, Flows in Networks (probabilistic), Highway Traffic, Parallel and distributed algorithms, Cellular Automata; 60K30, 90B15, 90B20, 68Q22", annote = "This work is part of our ongoing effort to design and implement a traffic simulation application capable of handling realistic problem sizes in multiple real-time. Our traffic simulation model includes multi-lane vehicular traffic and individual route-plans. On a 16-CPU SGI Power Challenger and a 12-CPU SUN workstation-cluster we have reached real-time for the whole German Autobahn network.", } @InProceedings{zpr97-307, author = "C. Gawron and S. Krau{\ss} and P. Wagner", institution = mi, title = "Dynamic User Equilibria in Traffic Simulation Models", booktitle = "Proceedings on Traffic and Granular Flow , Duisburg '97", editor = "M. Schreckenberg and D. E. Wolf", pages = "469--473", publisher = "Springer", year = "1997", crindex = "39,5,zpr97-307.ps.gz", keywords = "Highway traffic, Flows in networks (probabilistic), Statistical processes: Applications, Transport processes; 68U20, 60K30, 82C70, 90B15", annote = "We present an iterative algorithm to determine the dynamic user equilibrium for link costs given by a traffic simulation model. Each driver's route choice is modelled by a discrete probability distribution which is used to select a route in the simulation. After each simulation run, the probability distribution is adapted to minimize the perceived costs. As an example application, a dynamic version of Braess' paradox is studied.", } @TechReport{zpr97-306, author = "S. Krau{\ss}", institution = dlr, title = "Microscopic Traffic Simulation: Robustness of a Simple Approach", booktitle = "Proceedings on Traffic and Granular Flow , Duisburg '97", year = "1997", crindex = "578,15,zpr97-306.ps.gz", keywords = "Highway traffic, Statistical processes: Applications, Transport processes; 68U20, 60K30, 82C70", annote = "A family of microscopic traffic flow models is proposed. Each model is mainly characterized by the parameters a and b, describing the acceleration and deceleration capabilities of the vehicles. The model describes the phenomenon of jamming in a quite realistic way, if the parameters a and b correspond to realistic values of acceleration and deceleration.
The robustness of the model properties with respect to unrealistic choices of a and b is investigated. It is shown that qualitatively different types of behavior are found within the model family.", } @TechReport{zpr97-305, author = "S. Krau{\ss}", institution = dlr, title = "Towards a Unified View of Microscopic Traffic Flow Theories", year = "1997", crindex = "76,8,zpr97-305.ps.gz", keywords = "Highway traffic, Statistical processes: Applications, Transport processes; 68U20, 60K30, 82C70", annote = "Modeling and simulation of traffic has a long tradition. A vast number of different approaches have been used to simulate traffic, each of which has been calibrated and validated separately. This work aims at the way different models are interrelated. It is shown how one can, starting from very general modeling assumptions, construct a family of car following models that contains models closely related to well-known simulation models as special cases. Investigating this model family it can be shown, which models are qualitatively equivalent and which are not. This gives important hints as to which model approaches can in principle be unified.", } @Article{zpr97-304, author = "S. Krau{\ss} and P. Wagner and C. Gawron", institution = dlr, title = "Metastable States in a Microscopic Model of Traffic Flow", journal = "Physical Review E", volume = "55", number = "5", pages = "5597", month = may, year = "1997", crindex = "79,6,zpr97-304.ps.gz", keywords = "Highway traffic, Statistical processes: Applications, Transport processes; 60K30, 82C70", annote = "It is a well known fact that metastable states of very high throughput and hysteresis effects exist in traffic flow, which the simple cellular automaton (CA) model of traffic flow and its continuous generalization fail to reproduce. It is shown that the model can be generalized to give a one-parametric family of models, a part of which reproduces the metastable states and the hysteresis. The models having that property and those not having it are separated by a transition that can be clearly identified.", } @Article{zpr97-303, author = "S. Krau{\ss} and P. Wagner and C. Gawron", institution = mi, title = "Continuous Limit of the Nagel-Schreckenberg-Model", journal = "Physical Review E", volume = "54", number = "4", pages = "3707", month = oct, year = "1996", crindex = "68,7,zpr97-303.ps.gz", keywords = "Highway traffic, Statistical processes: Applications, Transport processes; 60K30, 82C70", annote = "A generalized version of the Nagel-Schreckenberg-Model of traffic flow is presented that allows for continuous values of the velocities and spatial co-ordinates. It is shown that this generalization reveals structures of the dynamics that are masked by the discreteness of the original model and thus helps to clarify the physical interpretation of the dynamics considerably. It is shown numerically that the transition leading from the free flow regime to the congested flow regime bears strong similarities with a first order phase transition in equilibrium thermodynamics. A similar behaviour is observed in more complicated microscopic models and in hydrodynamical descriptions of traffic flow, putting the model within a broader context of other models of traffic flow. An additional advantage of this continuous model is that it is much easier to calibrate with empirical data, only slightly decreasing numerical efficiency.", } @PhdThesis{zpr97-302, author = "J. Schepers", school = mi, title = "Exakte Algorithmen f{\"u}r orthogonale Packungsprobleme", year = "1997", crindex = "202k,95,zpr97-302.ps.gz", keywords = "packing, cutting, bin packing, strip packing, knapsack problem, 3-dimensional packing, interval graph, branch-and-bound; 05C90, 90B06, 90C27, 90C28, 90C35", annote = "Zahlreiche in Industrie und Wirtschaft auftretende Fragestellungen lassen sich als orthogonale Packungsprobleme formulieren. Dabei wird eine m{\"o}glichst g{\"u}nstige Anordnung einer Menge zwei- oder dreidimensionaler massiver Quader in einem oder mehreren Beh{\"a}ltern gesucht. Neben origin{\"a}r geometrischen Aufgaben wie dem Beladen von Paletten und Containern, dem Erstellen von Platinenlayouts oder dem Zuschnitt von Materialien (Cutting Stock Probleme) z{\"a}hlen hierzu auch Schedulingprobleme mit partitionierbaren Ressourcen.
Heuristiken liefern nur dann zufriedenstellende Ergebnisse, wenn alle Ma{\ss}e der zu packenden Teile wesentlich kleiner als die des Containers sind. Bereits ein einziges ung{\"u}nstig plaziertes sperriges Objekt kann die Qualit{\"a}t einer heuristischen L{\"o}sung bis hin zur Unbrauchbarkeit verschlechtern. Daher ist es erforderlich, Instanzen mit wenigen, sperrigen Teilen exakt zu l{\"o}sen.
Die in der Literatur beschriebenen exakten Verfahren beruhen auf ganzzahliger linearer Programmierung. Sie sto{\"s}en bereits bei sehr kleinen Instanzen an ihre Grenzen. In der vorliegenden Arbeiten pr{\"a}sentieren wir alternative Ans{\"a}tze, die auf zwei neuartige Konzepte st{\"u}tzen:

Numerische Resultate f{\"u}r zwei- und dreidimensionale Instanzen zeigen, da{\"s} damit erheblich gr{\"o}{\"s}ere Probleme als bisher exakt gel{\"o}st werden k{\"o}nnen.", } @InProceedings{zpr97-301, author = "A. Srivastav and K. Wolf", institution = inf, title = "Finding Dense Subgraphs with Semidefinite Programming", booktitle = "Approximation Algorithms for Combinatorial Optimization, Proceedings of APPROX 98", location = "Aalborg, Denmark", month = jul, editor = "K. Jansen and J. Rolim", series = "Lecture Notes in Computer Science", volume = "1444", publisher = "Springer-Verlag", pages = "181--191", year = "1998", keywords = "subgraph problem, approximation algorithms, randomized algorithms, semidefinite programming; 68Q25, 05C85", annote = "In this paper we consider the problem of computing the heaviest k-vertex induced subgraph of a given graph with nonnegative edge weights. This problem is known to be NP-hard, but its approximation complexity is not known.
For the general problem only an approximation ratio of Õ(n0.3885) has been proved (Kortsarz and Peleg, 1993). In the last years several authors analyzed the case $k=\Omega (n)$. In this case Asahiro et al. (1996) showed a constant factor approximation, and for dense graphs Arora et al. (1995) obtained even a polynomial-time approximation scheme.
We give a new approximation algorithm for arbitrary graphs and k = n/c for c > 1 based on semidefinite programming and randomized rounding which achieves for some c the presently best (randomized) approximation factors.", } @InProceedings{zpr97-300, author = "M. J{\"u}nger and G. Rinaldi", institution = inf, title = "Relaxations of the Max Cut Problem and Computation of Spin Glass Ground States", booktitle = "Proc. SOR '97", location = "Jena, Germany", year = "1998", pages = "74--83", editor = "P. Kischka", crindex = "60k,10,zpr97-300.ps.gz", annote = "This is a short survey. There is no abstract.", } @InProceedings{zpr97-299, author = "M. J{\"u}nger and E. K. Lee and P. Mutzel and T. Odenthal", institution = inf, title = "A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem", booktitle = "Proc. 5th International Symposium on Graph Drawing '97", location = "Rome, Italy", month = sep, year = "1997", editor = "G. Di Battista", series = "Lecture Notes in Computer Science", volume = "1353", publisher = "Springer-Verlag", pages = "13--24", crindex = "56k,12,zpr97-299.ps.gz", keywords = "crossing number, linear ordering, branch-and-cut;", annote = "We study the multi-layer crossing minimization problem from a polyhedral point of view. After the introduction of an integer programming formulation of the multi-layer crossing minimization problem, we examine the 2-layer case and derive several classes of facets of the associated polytope. Preliminary computational results for 2- and 3-layer instances indicate, that the usage of the corresponding facet-defining inequalities in a branch-and-cut approach may only lead to a practically useful algorithm, if deeper polyhedral studies are conducted.", } @Manual{zpr97-298, author = "S. Thienel", institution = inf, title = "{ABACUS} - {A} Branch-And-{CU}t System, Version 2.0, User's Guide and Reference Manual", year = "1997", crindex = "423k,350,zpr97-298.ps.gz", keywords = "combinatorial optimization, mixed integer programming, branch-and-cut; 68-04, 90C11, 90C27", annote = "ABACUS is a C++ framework for the implementation of branch-and-cut algorithms, branch-and-price algorithms, and their combination for linear mixed integer and combinatorial optimization problems. This manual explains the installation, the design, and the usage of the framework. Both the basic steps and advanced features are discussed. The reference manual describes all classes together with all members that are relevant for the user.", } @TechReport{zpr97-297, author = "V. Kaibel", institution = inf, title = "Polyhedral Combinatorics of {QAP}s with Less Objects than Locations (Extended Abstract)", year = "1997", crindex = "93k,10,zpr97-297.ps.gz", keywords = "polyhedral combinatorics, quadratic assignment problem, cutting plane algorithm; 90C09, 90C10, 90C27", annote = "For the classical quadratic assignment problem (QAP), where n objects have to be assigned to n locations (the n×n-case), polyhedral studies have been started in the very recent years by several authors. In this paper, we investigate the variant of the QAP, where the number of locations may exceed the number of objects (the m×n-case). It turns out that the polytopes that are associated with this variant are quite different from the ones associated with the n×n-case. However, one can obtain structural results on the m×n-polytopes by exploiting knowledge on the n×n-case, since the first ones are certain projections of the latter ones. Besides answering the basic questions for the affine hulls, the dimensions, and the trivial facets of the m×n-polytopes, we present a large class of facet defining inequalities. Employed into a cutting plane procedure, these polyhedral results enable us to compute optimal solutions for some hard instances from the QAPLIB for the first time without using branch-and-bound. Moreover, we can calculate for several yet unsolved instances significantly improved lower bounds.", } @Article{zpr97-296a, author = "C. Baur and S. P. Fekete", institution = mi, title = "Approximation of Geometric Dispersion Problems", journal = "invited to: Algorithmica", year = "1998", crindex = "141k,18,zpr97-296a.ps.gz", keywords = "computational geometry, geometric optimization, approximation algorithms, NP-completeness, packing, dispersion, bounds for approximation factors; 68Q25, 68U05, 90C28", annote = "We consider problems of distributing a number of points within a polygonal region P, such that the points are ``far away'' from each other. Problems of this type have been considered before for the case where the possible locations form a discrete set. Dispersion problems are closely related to packing problems. While Hochbaum and Maass (1985) have given a polynomial time approximation scheme for packing, we show that geometric dispersion problems cannot be approximated arbitrarily well in polynomial time, unless P=NP. We give a 2/3 approximation algorithm for one version of the geometric dispersion problem. This algorithm is strongly polynomial in the size of the input, i.e. its running time does not depend on the area of P. We also discuss extensions and open problems.", } @InProceedings{zpr97-296, author = "C. Baur and S. P. Fekete", institution = mi, title = "Approximation of Geometric Dispersion Problems", booktitle = "Short version in: Approximation Algorithms for Combinatorial Optimization (APPROX 98)", editor = "K. Jansen and J. Rolim", series = "Lecture Notes in Computer Science", volume = "1444", publisher = "Springer-Verlag", pages = "63--75", year = "1998", month = jul, location = "Aalborg, Denmark", crindex = "84k,12,zpr97-296.ps.gz", keywords = "computational geometry, geometric optimization, approximation algorithms, NP-completeness, packing, dispersion, bounds for approximation factors; 68Q25, 68U05, 90C28", annote = "We consider problems of distributing a number of points within a polygonal region P, such that the points are ``far away'' from each other. Problems of this type have been considered before for the case where the possible locations form a discrete set. Dispersion problems are closely related to packing problems. While Hochbaum and Maass (1985) have given a polynomial time approximation scheme for packing, we show that geometric dispersion problems cannot be approximated arbitrarily well in polynomial time, unless P=NP. We give a 2/3 approximation algorithm for one version of the geometric dispersion problem. This algorithm is strongly polynomial in the size of the input, i.e. its running time does not depend on the area of P. We also discuss extensions and open problems.", } @TechReport{zpr97-295, author = "B. Knab and R. Schrader and I. Weber and K. Weinbrecht and B. Wichern", institution = mi, title = "Ein Mesoskopisches Simulationsmodell zur Kollektivfortschreibung", year = "1997", crindex = "43k,10,zpr97-295.ps.gz", keywords = "cluster analysis, single link, complete link, network-flows; 62H30, 90A09, 90A19, 90B10, 92G30", annote = "Vorgestellt wird ein am ZPR neu entwickeltes Simulationsmodell zur Fortschreibung von Bausparkollektiven, das Vertr{\"a}ge mit {\"a}hnlichem Sparverhalten in Gruppen zusammenfa{\ss}t und auf Einzelkonten basiert. Zum einen wird erl{\"a}utert, wie mit Hilfe von Clusteranalyse Prototypen bestimmt werden, die das Sparverhalten der Schichten angeben, zum anderen wird gezeigt, wie anschlie{\ss}end ein gegebener Bestand an Bausparvertr{\"a}gen mittels eines Minimum-Cost-Flow-Algorithmus den definierten Schichten zugeordnet wird. Das beschriebene Modell eignet sich sowohl f{\"u}r kurz- als auch f{\"u}r langfristige Simulationen.", } @Misc{zpr97-294, author = "W. Hochst{\"a}ttler", institution = mi, title = "Duality in Combinatorial Optimization -- Sometimes it Works, Sometimes it Won't", year = "1997", crindex = "122k,57,zpr97-294.ps.gz", keywords = "duality, linear programming, matroids, oriented matroids, polarity, adjoints, skew fields, pseudomodular matroids, cooperative game, core, Held-Karp Bound, minimal spanning tree problem, traveling salesman problem, Nucleon, Matching; 05B35, 06C10, 52B40, 12E15, 90C27, 90D12", annote = "In this thesis we comment on six papers, three from matroid theory and three from cooperative game theory. Their common theme is duality in combinatorial optimization, although it occurs in different settings.
The first three articles (available as 92-109, 94-154 and 95-195) study polarity (or projective duality) in oriented matroids, a combinatorial model for linear programming and hyperplane arrangements. While older work on adjoints contains mainly negative results on the existence of adjoints, we provide several sufficient conditions, in particular in the rank four case.
In cooperative game theory (see 93-137, 94-166 and 94-178) we study several solution concepts which are defined by polyhedral constraints. These concepts are applied to games defined by combinatorial optimization problems, such as the TSP, the MCMST and non-bipartite matching.", } @PhdThesis{zpr97-293, author = "A. Hamacher", school = mi, title = "Baumzerlegungen unter Nebenbedingungen -- Ein Clusterverfahren zur {L}{\"o}sung praktischer Vehicle-Routing-Probleme", year = "1997", crindex = "641k,147,zpr97-293.ps.gz", keywords = "tree partition,clustering, dynamic programming, complexity, vehicle routing; 05C05, 68Q25, 90B06, 90C27, 90C39", annote = "Kombinatorische Optimierungsprobleme, die bei Fragestellungen aus der Praxis auftreten, sind meist schwer zu l{\"o}sen. Als besonders schwer in dieser Klasse gilt die Gruppe der Vehicle-Routing-Probleme (VRPs). Schon bei kleinen Probleminstanzen mit wenigen Kunden werden hier die Grenzen der exakten L{\"o}sbarkeit erreicht. Daraus ergibt sich, da{\ss} in praktischen VRPs mit gr{\"o}{\ss}eren Kundenmengen nur heuristische Ans{\"a}tze Verwendung finden k{\"o}nnen.
Das im Mittelpunkt dieser Arbeit stehende Clusterverfahren entstand im Rahmen der Entwicklung eines Dispositionssystemes f{\"u}r eine Spedition der Lebensmittelbranche. Als die wesentliche Eigenschaft der dabei zu erstellenden Tourenpl{\"a}ne wurde die regionale Begrenzung der Auslieferungsgebiete f{\"u}r die einzelnen Fahrzeuge vorgeschrieben. Wir w{\"a}hlten daher die zur L{\"o}sung von VRPs g{\"a}ngige Vorgehensweise des Cluster first - Route second. Hierbei werden die zu beliefernden Kunden zun{\"a}chst zu Clustern zusammengefa{\ss}t, um darauf aufbauend die Reihenfolge der Kunden eines Clusters, also die Touren bestimmen zu k{\"o}nnen.
Das sich uns damit stellende Problem der Bestimmung von regional begrenzten Kundenclustern formulierten wir mathematisch als Baumzerlegungsproblem unter Nebenbedingungen. Erste Resultate waren ein allgemeiner NP-Vollst{\"a}ndigkeitsbeweis und ein heuristischer Greedyansatz, der als Verallgemeinerung des von Kundu und Misra vorgeschlagenen Verfahrens zur Zerlegung von B{\"a}umen mit einer Gewichtsfunktion aufgefa{\ss}t werden kann. Detailliertere Auseinandersetzungen mit dem Problem, den Praxisdaten und den NP-Vollst{\"a}ndigkeitsbeweisen ergaben eine Unterscheidung der Baumzerlegungsprobleme sowohl nach dem Knotengrad der untersuchten B{\"a}ume als auch nach der Anzahl der Gewichtsfunktionen. Unter diesen Gesichtspunkten war es uns m{\"o}glich, eine vollst{\"a}ndige Klassifizierung der Baumzerlegungsprobleme unter Nebenbedingungen in Komplexit{\"a}tsklassen zu erstellen:
NP-vollst{\"a}ndig im strengen Sinne ist das Baumzerlegungsproblem f{\"u}r Instanzen, bei denen die Anzahl der Gewichtsfunktionen mit der Problemgr{\"o}{\ss}e w{\"a}chst. Bei B{\"a}umen mit mindestens zwei Gewichtsfunktionen und unbeschr{\"a}nktem Knotengrad wird die Fragestellung zu einem Number-Problem. Es gelang uns hier, das Knapsack-Problem auf diese Teilklasse zu reduzieren und durch Angabe eines dynamischen Programmes die Pseudopolynomialit{\"a}t nachweisen. Bei Probleminstanzen mit einer Gewichtsfunktion ist der von Kundu und Misra beschriebene lineare Greedy-Algorithmus optimal. F{\"u}r den bei der Clusterung auftretenden praxisrelevanten Fall der Zerlegung knotengradbeschr{\"a}nkter B{\"a}ume mit einer beschr{\"a}nkten Anzahl von Gewichtsfunktionen konnten wir ein exaktes polynomielles Verfahren entwickeln, das auf die Ideen des Greedyansatzes aufbaut.
Die Implementation dieses Verfahrens lieferte auf den uns vorliegenden Datens{\"a}tzen der zuvor erw{\"a}hnten Spedition hervorragende Laufzeitresultate. Diese guten Ergebnisse konnten auch durch Anwendung des Verfahrens auf Planungsdaten einer weiteren Spedition best{\"a}tigt werden.
Die vorliegende Arbeit gliedert sich in zwei Teile. Zun{\"a}chst entwickeln wir im theoretischen Teil ein exaktes polynomielles Verfahren f{\"u}r Baumzerlegungen unter Nebenbedingungen. Im praxisorientierten zweiten Teil wenden wir dieses Verfahren an, um in zwei Vehicle-Routing-Problemen aus der Praxis eine regionale Clusterung der Kunden vorzunehmen.
Der erste Teil beginnt mit einer Einf{\"u}hrung der verwendeten Begriffe aus der Graphen- und Komplexit{\"a}tstheorie. Es folgt die exakte Definition des Baumzerlegungsproblemes unter Nebenbedingungen. Abschnitt 3.2 stellt die oben erw{\"a}hnten NP-Vollst{\"a}ndigkeitsbeweise sowie das dynamische Programm f{\"u}r Baumzerlegungen mit konstanter Anzahl von Gewichtsfunktionen vor. Das exakte Verfahren zur L{\"o}sung von Baumzerlegungen mit beschr{\"a}nkter Anzahl von Gewichtsfunktionen auf knotengradbeschr{\"a}nkten B{\"a}umen beschreiben wir in Abschnitt 3.4. Zun{\"a}chst erl{\"a}utern wir den generischen Basisalgorithmus, der den in diesem Kapitel aufgezeigten Verfahren zugrunde liegt. Die Darstellung des optimalen Greedy-Verfahrens f{\"u}r eine Gewichtsfunktion sowie dessen Verallgemeinerung, die unseren ersten Ansatz zur L{\"o}sung des Problemes darstellte, folgen. In Abschnitt 3.4.4 veranschaulichen wir das exakte Verfahren zun{\"a}chst am Beispiel zweier Gewichtsfunktionen auf bin{\"a}ren B{\"a}umen. Hier enth{\"a}lt die Laufzeitabsch{\"a}tzung bereits alle wesentlichen Ideen des allgemeinen Falles, ist aber deutlich einfacher nachzuvollziehen. Die ausf{\"u}hrliche Darstellung und Analyse des polynomiellen Verfahrens zur L{\"o}sung der Baumzerlegungen bei beschr{\"a}nktem Knotengrad und beschr{\"a}nkter Anzahl von Knotengewichtsfunktionen schlie{\ss}t sich an. Das Kapitel endet mit Laufzeitanalysen auf zuf{\"a}lligen Instanzen, die mit den theoretischen Ergebnissen verglichen werden.
Der zweite Teil der Arbeit besch{\"a}ftigt sich mit der Anwendung der Baumzerlegungen unter Nebenbedingungen auf VRPs. Abschnitt 4.1 definiert das VRP und gibt einen {\"U}berblick {\"u}ber die Vielfalt m{\"o}glicher Fragestellungen in diesem Bereich. Abschnitt 4.2 erl{\"a}utert dann, wie mit Hilfe von Baumzerlegungen die regionale Clusterung der Transportauftr{\"a}ge und die damit verbundene Zuordnung zu den einzelnen Fahrzeugen vorgenommen werden kann. Das Tourenplanungsproblem der Lebensmittelspedition sowie das zweite Anwendungsbeispiel f{\"u}r das Clusterverfahren beschreiben wir in den Abschnitten 4.3 und 4.4. Danach entwickeln wir eine Startheuristik f{\"u}r das erste Anwendungsproblem, in dem enge Zeitfenstervorgaben die Tourenzusammenstellung erschweren und geben einen {\"U}berblick {\"u}ber m{\"o}gliche Verbesserungsverfahren. Die Planungsresultate werden in Abschnitt 4.6 zusammengestellt. Wir schlie{\ss}en die Arbeit mit einer Zusammenfassung unserer Ergebnisse.", } @Article{zpr97-292, author = "M. Diehl and M. J{\"u}nger and R. Fr{\"u}hwirth and J. Scherzer", institution = inf, title = "Global optimization for track finding", journal = "Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment", number = "389", pages = "180--183", year = "1997", } @InCollection{zpr97-291, author = "M. J{\"u}nger and G. Reinelt and G. Rinaldi", institution = inf, title = "The Traveling Salesman Problem", booktitle = "Annotated bibliographies in combinatorial optimization", editor = "M. Dell'Amico and F. Maffioli and S. Martello", publisher = "John Wiley \& Sons", pages = "199--221", year = "1997", annote = "This is an annotated bibliography. There is no abstract.", } @Article{zpr97-290, author = "S. P. Fekete and J. Schepers", institution = mi, title = "On more-dimensional packing {III}: Exact Algorithms", journal = "submitted to: Discrete Applied Mathematics", year = "1997", keywords = "packing, 3-dimensional geometry, exact algorithms, branch-and-bound, geometric optimization, interval graphs; 90C28, 68R99", annote = "More-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a two-level tree search algorithm for solving more-dimensional packing problems to optimality. Computational results are reported, including optimal solutions for all two-dimensional test problems from recent literature.", } @Article{zpr97-289, author = "S. P. Fekete and J. Schepers", institution = mi, title = "On more-dimensional packing {II}: Bounds", journal = "submitted to: Discrete Applied Mathematics", year = "1997", keywords = "packing, 3-dimensional geometry, exact algorithms, branch-and-bound, geometric optimization, interval graphs; 90C28, 68R99", annote = "More-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is of crucial importance to have good and easy lower bounds for an optimal solution. Previous efforts have produced a number of special classes of such bounds. Unfortunately, some of these bounds are somewhat complicated and hard to generalize. We present a new approach for obtaining classes of lower bounds for more-dimensional packing problems; our bounds improve and simplify on several well-known bounds from previous literature. In addition, our approach provide an easy framework for proving correctness of new bounds.", } @Article{zpr97-288, author = "S. P. Fekete and J. Schepers", institution = mi, title = "On more-dimensional packing {I}: Modeling", journal = "submitted to: Discrete Applied Mathematics", year = "1997", keywords = "packing, 3-dimensional geometry, exact algorithms, branch-and-bound, geometric optimization, interval graphs; 90C28, 68R99", annote = "More-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for practical exact algorithms have been unable to avoid structural problems that appear for packing problems in two- or higher-dimensional space. We present a new approach for modeling packings, using a graph-theoretical characterization of feasible packings. Our characterization allows it to deal with classes of packings that share a certain combinatorical structure, instead of single ones. This allows it to make it the basis for a succesful branch-and-bound framework.", } @TechReport{zpr97-287, author = "B. Schwikowski and E. Speckenmeyer", institution = inf, title = "On computing all minimal solutions for feedback problems", year = "1997", crindex = "64k,10,zpr97-287.ps.gz", keywords = "feedback problem, directed graph, exact enumeration problem; 68Q25,05C85,05C38,05C20,68Q35,05A15", annote = "We present an algorithm that generates all (inclusion-wise) minimal feedback vertex sets of a directed graph G=(V,E). The feedback vertex sets of G are generated with a polynomial delay of O(|V|2(|V|+|E|)). Variants of the algorithm generate all minimal solutions for the undirected case and the directed feedback arc set problem, both with a polynomial delay of O(|V|,|E|,(|V|+|E|).", } @TechReport{zpr97-286, author = "W. Hochst{\"a}ttler and J. Nesetril", institution = mi, title = "Menger's Theorem as Morphism Duality", year = "1997", crindex = "37k,5,zpr97-286.ps.gz", keywords = "matroids, strong map, homomorphism, duality, Menger's theorem; 05B35, 05B40, 05C38, 05C70, 18B99, 90C27", annote = "The purpose of this note is to point out that Menger's Theorem in a quite natural way gives an example of a morphism duality. In this setting it is the simple equation
(C_k,e) --> = -/-> (C_{k+1},e).
", } @TechReport{zpr97-285, author = "M. J{\"u}nger and V. Kaibel", institution = inf, title = "Box-Inequalities for Quadratic Assignment Problems", year = "1997", crindex = "158k,21,zpr97-285.ps.gz", keywords = "quadratic assignment problem, polyhedral combinatorics, QAP-polytope, facets, cutting plane procedure; 90C09, 90C10, 90C27", annote = "Linear Programming based lower bounds have been considered both for the general as well as for the symmetric quadratic assignment problem several times in the recent years. They have turned out to be quite good in practice. Investigations of the polytopes underlying the corresponding integer linear programming formulations (the non-symmetric and the symmetric quadratic assignment polytope) have been started by Rijal (1995), Padberg and Rijal (1996), and J{\"u}nger and Kaibel (1996, 1997). They have lead to basic knowledge on these polytopes concerning questions like their dimensions, affine hulls, and trivial facets. However, no large class of (facet-defining) inequalities that could be used in cutting plane procedures had been found. We present in this paper the first such class of inequalities, the box inequalities, which have an interesting origin in some well-known hypermetric inequalities for the cut polytope. Computational experiments with a cutting plane algorithm based on these inequalities show that they are very useful with respect to the goal of solving quadratic assignment problems to optimality or to compute tight lower bounds. The most effective ones among the new inequalities turn out to be indeed facet-defining for both the non-symmetric as well as for the symmetric quadratic assignment polytope.", } @TechReport{zpr97-284, author = "M. J{\"u}nger and V. Kaibel", institution = inf, title = "The {QAP}-Polytope and the Star-Transformation", year = "1997", crindex = "161k,22,zpr97-284.ps.gz", keywords = "quadratic assignment problem, polyhedral combinatorics, QAP-polytope; 90C09, 90C10, 90C27", annote = "Polyhedral Combinatorics has been successfully applied to obtain considerable algorithmic progress towards the solution of many prominent hard combinatorial optimization problems. Until very recently, the quadratic assignment problem (QAP) was one of the few exceptions. Recent work of Rijal (1995) and Padberg and Rijal (1996) has on the one hand yielded some basic facts about the associated quadratic assignment polytope, but has on the other hand shown that investigations even of the very basic questions (like the dimension, the affine hull, and the trivial facets) soon become extremely complicated. In this paper, we propose an isomorphic transformation of the ``natural'' realization of the quadratic assignment polytope, which simplifies the polyhedral investigations enormously. We demonstrate this by giving short proofs of the basic results on the polytope that indicate that, exploiting the techniques developed in this paper, deeper polyhedral investigations of the QAP now become possible. Moreover, an ``inductive construction'' of the QAP-Polytope is derived that might be useful in branch-and-cut algorithms.", } @TechReport{zpr97-283, author = "A. Hamacher and W. Hochst{\"a}ttler and C. Moll", institution = mi, title = "Tree Partitioning under Constraints - Clustering for Vehicle Routing Problems", year = "1997", crindex = "87k,15,zpr97-283.ps.gz", keywords = "tree partition, clustering, dynamic programming, complexity, vehicle routing; 05C05, 68Q25, 90B06, 90C27, 90C39", annote = "We present a dynamic programming algorithm for the following problem: Given a tree T=(V,E), a set of q non-negative integer weights wi:V -> N on the nodes, and a threshold Ri, i=1,...,q. Partition the vertices of the tree into connected components T0,..., Tk, such that for all i in {1,...,q}, j in {0,...,k} sum_{v in Tj} wi(v) <= Ri and k is minimal. We show that this problem is hard, if q is unbounded or if T has unbounded maximum degree. In all other cases the running time of the dynamic program has a polynomial worst-case bound.", } @Article{zpr97-282, author = "W. Hochst{\"a}ttler and B. Jackson", institution = mi, title = "Large Circuits in Binary Matroids of Large Cogirth: {II}", journal = "Journal of Combinatorial Theory B", year = "1998", month = sep, volume = "74", number = "1", pages = "53--63", crindex = "56k,10,zpr97-282.ps.gz", keywords = "circuit, binary matroid; 05B35, 05C38", annote = "Let F7 denote the Fano matroid and M be a simple connected binary matroid such that every cocircuit of M has size at least d>=3. We show that if M does not have an F7-minor, M is not F7*, and d is not in {5,6,7,8}, then M has a circuit of size at least min{r(M)+1,2d}. We conjecture that the latter result holds for all d>=3.", } @Article{zpr97-281, author = "W. Hochst{\"a}ttler and B. Jackson", institution = mi, title = "Large Circuits in Binary Matroids of Large Cogirth: {I}", journal = "Journal of Combinatorial Theory B", year = "1998", month = sep, volume = "74", number = "1", pages = "35--52", crindex = "73k,17,zpr97-281.ps.gz", keywords = "hamiltonicity, binary matroid; 05B35, 05C45", annote = "Let F7 denote the Fano matroid and e be a fixed element of F7. Let P(F7,e) be the family of matroids obtained by taking the parallel connection of one or more copies of F7 about e. Let M be a simple binary matroid such that every cocircuit of M has size at least d >= 3. We show that if M does not have an F7-minor, M is not F*7 and d >= (r(M)+1)/2 then M has a circuit of size r(M)+1. We also show that if M is connected, e in E(M), M does not have both an F7-minor and an F*7-minor, and M is not in P(F7,e), then M has a circuit containing e and of size at least d+1.", } @Article{zpr97-280, author = "S. P. Fekete and J. S. B. Mitchell", institution = mi, title = "Histogram decomposition and stereolithography", journal = "submitted to: International Journal of Computational Geometry and Applications", year = "1997", crindex = "68k,13,zpr97-280.ps.gz", keywords = "computational geometry, NP-completeness, complexity, dynamic programming, 3-dimensional geometry, surface decomposition, histograms, terrains, stereolithography, manufacturing processes, NC-machining, visibility; 68Q25, 68U05, 90C28, 90C39", annote = "A polyhedral solid model can be constructed by the process of stereolithography if it has a facet so that all points of the model can see this facet, in the direction orthogonal to it; such a polyhedron is a histogram. In stereolithography, or other forms of layered manufacturing, one may want to decompose a model into a small number of histograms. In this note, we provide the first algorithmic results on the histogram decomposition problem, proving that it is NP-complete to decide if a model can be decomposed into k histograms, if the model is either a polygonal region (with holes) in the plane, or a solid polyhedral model of genus 0.", } @TechReport{zpr97-279, author = "F. Brockners", institution = mi, title = "Bulk multicast data transfer - towards the integration of {FEC} and {ARQ} using a lightweight feedback control tree", month = jul, year = "1997", crindex = "246k,13,zpr97-279.ps.gz", keywords = "reliable multicast, feedback aggregation, forward error correction (FEC);", annote = "This paper describes the design of a reliable multicast framework which integrates FEC and receiver-initiated retransmit to ensure reliability. A dynamically elected control tree is used to aggregate the NAKs and tackle the NAK implosion problem. Both techniques support flow and congestion control to enable efficient, high data rate multicast data transfer as performance measurements with our prototype show. The presented protocol uses NAK-feedback to handle burst packet loss and to adjust the send rate to a level, where most of the losses can be recovered through FEC-coding. Upstream feedback is reduced to a minimum allowing scalability with very limited protocol processing. The responsibility for the reliable data transfer is completely moved to the receivers. Receivers avoid state management for other group members, which is common in the design of other tree-based approaches.", } @InProceedings{zpr97-278, author = "M. J{\"u}nger and S. Leipert and P. Mutzel", institution = inf, title = "Pitfalls of using {PQ}-trees in Automatic Graph Drawing", booktitle = "Proc. 5th International Symposium on Graph Drawing '97", location = "Rome, Italy", month = sep, year = "1997", editor = "G. Di Battista", series = "Lecture Notes in Computer Science", volume = "1353", pages = "193--204", publisher = "Springer-Verlag", crindex = "112k,12,zpr97-278.ps.gz", keywords = "PQ-trees, maximal planar subgraphs, planarization, level-planar dags; 05C85, 68R10, 90C35", annote = "A number of erroneous attempts involving PQ-trees in the context of automatic graph drawing algorithms have been presented in the literature in recent years. In order to prevent future research from constructing algorithms with similar errors we point out some of the major mistakes.
In particular, we examine erroneous usage of the PQ-tree data structure in algorithms for computing maximal planar subgraphs and an algorithm for testing leveled planarity of leveled directed acyclic graphs with several sources and sinks.", } @TechReport{zpr97-277, author = "U. Heinrichs and C. Moll", institution = mi, title = "On the scheduling of one-dimensional transport systems", year = "1997", crindex = "78k,18,zpr97-277.ps.gz", keywords = "scheduling, shortest path, cran, galvanization, production planning, transportation; 05C38, 05C85, 68R10, 90B30, 90B35", annote = "In this paper we consider the problem of finding a feasible routing for one-dimensional transport systems. This problem arises as a subproblem in production planning, when a mono-rail crane with several crabs is part of the production lane. Practical restrictions like finite speed of crabs and a minimal distance between crabs lead to a special routing problem.
We show that this problem corresponds to the geometric problem of covering segments with angle-restricted curves with the additional constraint that all curves have at least distance 1. We prove that this question can be formulated as a shortest path problem.
Finally we discuss how the presented algorithm can be used as a module for a greedy-algorithm solving a no-wait scheduling problem.", } @Article{zpr97-276a, author = "E. J. Anderson and S. P. Fekete", institution = mi, title = "Two-Dimensional Rendezvous Search", journal = "to appear: Operations Research", year = "1998", crindex = "96k,30p,zpr97-276a.ps.gz", keywords = "search problems, rendevous search, dynamic games; 90B40, 65K10", annote = "We consider rendezvous problems in which two players move on the plane and wish to cooperate in order to minimise their first meeting time. We begin by considering the case when they know that they are a distance d apart, but they do not know the direction in which they should travel. We also consider a situation in which player 1 knows the initial position of player 2, while player 2 is only given information on the initial distance of player 1. Finally we give some results for the case where one of the players is placed at an initial position chosen equiprobably from a finite set of points.", } @InProceedings{zpr97-276, author = "E. J. Anderson and S. P. Fekete", institution = mi, title = "Asymmetric Rendezvous on the Plane", booktitle = "Proceedings of the Fourteenth Annual Symposium on Computational Geometry, June 7-10, 1998, Minneapolis, Minnesota, USA", pages = "365--373", publisher = "ACM Press", year = "1998", crindex = "89k,15p,zpr97-276.ps.gz", keywords = "search problems, rendevous search, dynamic games; 90B40, 65K10", annote = "We consider rendezvous problems in which two players move on the plane and wish to cooperate in order to minimise their first meeting time. We begin by considering the case when they know that they are a distance d apart, but they do not know the direction in which they should travel. We also consider a situation in which player 1 knows the initial position of player 2, while player 2 is only given information on the initial distance of player 1. Finally we give some results for the case where one of the players is placed at an initial position chosen equiprobably from a finite set of points.", } @InCollection{zpr97-275, author = "B. Steckemetz", institution = mi, title = "Adaptive Skelettierung handgeschriebener Zeichen", booktitle = "to appear in: Tagungsband zur DAGM 1997", year = "1997", crindex = "51k,8,zpr97-275.ps.gz", keywords = "pattern recognition, character recognition, handwriting recognition; 68U", annote = "In der Literatur hat sich die Auffassung durchgesetzt, da{\ss} zur Skelettierung von Bin{\"a}rbildern verschiedene Algorithmen eingesetzt werden k{\"o}nnen, die jeweils Vor- und Nachteile besitzen. Anhand von handgeschriebenen Zeichen wird hier ein neuer Algorithmus vorgestellt, der bei der Skelettierung der Zeichen gegen{\"u}ber anderen Verfahren deutlich bessere Resultate liefert. Die gew{\"u}nschte Genauigkeit und damit auch die Menge an Artefakten ist durch einen Parameter bestimmbar. Zur Segmentierung von Zeichen in verzweigungsfreie Linien existiert eine einfachere und schnellere Variante des Algorithmus.", } @TechReport{zpr97-274, author = "B. Steckemetz", institution = mi, title = "Neighbor Features for fast Teach-In of Color Image Sequences", year = "1997", crindex = "125k,6,zpr97-274.ps.gz", keywords = "pattern recognition, image processing; 68T", annote = "We present an algorithm for classification and a fast teach-in of ready-made food in the industrial food production. We show that simple color features are not suitable in the case of complex colored objects and can not represent the geometric arrangement of components. Neighbor features perform well on these tasks and help to reduce the user interaction during teach-in to a minimum. A fast preprocessing keeps the calculation time below one second on standard PC hardware.", } @InProceedings{zpr97-273, author = "S. P. Fekete and M. Houle and S. Whitesides", institution = mi, title = "The wobbly logic engine: proving hardness of non-rigid geometric graph representations", booktitle = "Graph Drawing, Proc. 5th International Symposium, GD '97", location = "Rome, Italy", month = sep, year = "1997", series = "Lecture Notes in Computer Science", volume = "1353", publisher = "Springer-Verlag", pages = "272--283", crindex = "306k,20,zpr97-273.ps.gz", keywords = "complexity, NP-hardness, logic engine, graph representation, visibility, graph drawing, 3-dimensional geometry; 05C10, 05C75, 68R05, 68R10", annote = "In this paper we describe a general technique for establishing NP-hardness of graph representations. This technique is a generalization of the tool called the logic engine. We show that it is possible to extend it to a wobbly logic engine,which provides a proof method of NP-hardness for a variety of graph representations for which the set of feasible representations does not have to be discrete. This includes representations by visibility and intersection. In particular, we give a first proof that it is NP-hard to decide whether a graph has a nondegenerate z-axis parallel visibility representation (ZPR) by unit squares.", } @TechReport{zpr97-272, author = "W. Hochst{\"a}ttler", institution = mi, title = "About the Tic-Tac-Toe Matroid", year = "1997", crindex = "38k,5,zpr97-272.ps.gz", keywords = "algebraic matroids, duality; 05B35, 11J85, 51E25", annote = "The purpose of this note is to make a problem, already mentioned in M. Alfter, W. Hochst{\"a}ttler [Discrete Applied Mathematics, 60 (1995)], more tangible. We introduce a matroid which has ``the'' combinatorial properties of algebraic matroids as derived in A.W.M. Dress, L. Lovász [Combinatorica, 7 (1987)], the dual of which is non-algebraic. Therefore, it seems to be a good candidate for a negative answer to the old problem whether algebraic matroids are closed under duality (see e.g. J. Oxley [Matroid Theory (1992)] 6.7.15).", } @Article{zpr97-271, author = "M. J{\"u}nger and G. Rinaldi and S. Thienel", institution = inf, title = "Practical Performance of Efficient Minimum Cut Algorithms", journal = "to appear in: Algorithmica", year = "1997", crindex = "260k,27,zpr97-271.ps.gz", keywords = "minimum cut algorithm, graph algorithm; 05C80, 90B10, 90C27, 90C35", annote = "In the late eighties and early nineties, three major exciting new developments (and some ramifications) in the computation of minimum capacity cuts occurred and these developments motivated us to evaluate the old and new methods experimentally. We provide a brief overview of the most important algorithms for the minimum capacity cut problem and compare these methods both on problem instances from the literature and on problem instances originating from the solution of the traveling salesman problem by branch-and-cut.", } @Article{zpr97-270, author = "J. Franco and J. Goldsmith and J. Schlipf and E. Speckenmeyer and R. P. Swaminathan", institution = inf, title = "An algorithm for the class of pure implicational formulas", journal = "Discrete Applied Mathematics", volume = "96-97", number = "1-3", year = "1999", pages = "89--106", keywords = "satisfiability, implicational formulas,fixed parameter tractable, Boolean functions;", annote = "Heusch introduced the notion of pure implicational formulas. He showed that the falsifiability problem for pure implicational formulas with k negations is solvable in time O(n). Such falsifiability results are easily transformed to satisfiability results on CNF formulas. We show that the falsifiability problem for pure implicational formulas is solvable in time O(kn), which is polynomial for a fixed k. Thus this problem is fixed-parameter tractable.", } @Article{zpr97-269, author = "F. Meisgen", institution = inf, title = "Dynamic Load Balancing for Simulations of Biological Aging", journal = "International Journal of Modern Physics C", volume = "8", number = "3", pages = "575--582", month = jun, year = "1997", crindex = "158k,10,zpr97-269.ps.gz", keywords = "dynamic load balancing, heterogeneous system, simulation, biological aging; 68Q22, 68U20", annote = "The efficient usage of parallel computers and workstation clusters for biologically motivated simulations depends first of all on a dynamic redistribution of the workload. For the development of a parallel algorithm for the Penna model of aging we have used a dynamic load balancing library, called PLB. It turns out that PLB manages a nearly balanced load situation during runtime taking only a low communication overhead. We compare different architectures like parallel computers and nondedicated heterogeneous networks, and give some results for large populations.", } @InProceedings{zpr97-268, author = "A. Bachem and M. Bodmann and G. Bolz and T. Emden-Weinert and A. Erdmann and B. Monien and M. Kiahaschemi and H. J. Pr{\"o}mel and J. Schepers and R. Schrader and J. Schulze and S. Tsch{\"o}ke", booktitle = "Paralleles H{\"o}chstleistungsrechnen und seine Anwendungen", note = "Beitrag zur Statustagung des BMBF, IIPSC 97", title = "Verbundprojekt {PARALOR}: Parallele Verfahren zur Wegoptimierung in Flugplanung und Logistik", year = "1997", crindex = "106k,18,zpr97-268.ps.gz", keywords = "parallel algorithms, fleet assignment, crew scheduling, vehicle routing, 3-dimensional packing, branch-and-bound, simulated trading; 90B06, 90B35, 90C08", annote = "Die L{\"o}sung kombinatorischer Optimierungsprobleme ist in vielen Bereichen von Wirtschaft und Technik der Schl{\"u}ssel zur Steigerung der Effizienz technischer Abl{\"a}ufen, zur Verbesserung der Produktqualit{\"a}t und zur Veringerung von Produktions-, Material- und Transportkosten. Der Einsatz herk{\"o}mmlicher sequentieller Verfahren ist f{\"u}r praxisrelevante Probleme aufgrund der enormen Rechenzeiterfordernisse nur sehr eingeschr{\"a}nkt m{\"o}glich. Parallele Systeme bieten eine M{\"o}glichkeit, derartige Probleme in vertretbarer Zeit zu l{\"o}sen. Im Rahmen des Verbundprojektes PARALOR wird untersucht, wie parallele Algorithmen der kombinatorischen Optimierung in konkreten, industriellen Anwendungen aus der Flugplanung sowie der Speditionslogistik effizient eingesetzt werden k{\"o}nnen. In diesem Artikel werden wesentliche Ergebnisse des Projekts exemplarisch vorgestellt.", } @InProceedings{zpr97-267, author = "S. P. Fekete and J. Schepers", institution = mi, title = "A new exact algorithm for general orthogonal d-dimensional knapsack problems", booktitle = "Algorithms - ESA '97, 5th Annual European Symposium", location = "Graz, Austria", editors = "R. Burkard and G. J. Woeginger", series = "Lecture Notes in Computer Science", volume = "1284", publisher = "Springer-Verlag", pages = "144--156", year = "1997", crindex = "63k,11,zpr97-267.ps.gz", keywords = "packing, 3-dimensional packing, exact algorithm, branch-and-bound, geometric optimization, interval graph; 90C28, 68R99", annote = "The d-dimensional orthogonal knapsack problem (OKP) has a wide range of practical applications, including packing, cutting and scheduling. We present a new approach to this problem, using a graph-theoretical characterization of feasible packings. This characterization allows us to deal with classes of packings that share a certain combinatorical structure, instead of single ones. Combining the use of this structure with other heuristics, we develop a two-level tree search algorithm for finding exact solutions for the d-dimensional OKP. Computational results are reported, including optimal solutions for all two-dimensional test problems from recent literature.", } @TechReport{zpr97-266, author = "S. P. Fekete and M. Schmitt", institution = mi, title = "Traveling Salesmen in the Age of Competition", year = "1997", crindex = "35k,5,zpr97-266.ps.gz", keywords = "Traveling salesman problem, combinatorial games; 90D43, 90D46", annote = "We propose the ``Competing Salesmen Problem'' (CSP), a 2-player competitive version of the classical Travelling Salesman Problem. This problem arises when we are considering two competing salesmen instead of just one. The concern for a shortest tour is replaced by the necessity to reach any of the customers before the opponent does.
In particular, we consider the situation where players are taking turns, moving one edge at a time within a graph G=(V,E). The set of customers is given by a subset VC of the vertices V. At any given time, both players know of their opponent's position. A player wins if he is able to reach more vertices of VC before the opponent does.
We prove that certain decision problems of this type are NP-complete; we conjecture that the general problem is PSPACE-complete. Furthermore, we show that the starting player may lose the game, even if both players start from the same vertex. For special cases, we can give a number of positive results:
If G is a tree T and both players start from the same vertex, we can show that the starting player can avoid a loss. On the other hand, we can show that the second player can avoid to lose by more than one customer, provided that VC consists of leaves of the tree T. It is unclear whether a polynomial strategy exists for any of the two players to force this outcome, and we point out some of the difficulties. For the case where T is a star (i.e. a tree with only one vertex of degree higher than 2) and VC consists of n leaves of T, we give a simple and fast O(n log n) strategy which is optimal for both players.
We conclude by discussing geometric variants of the problem.", } @InProceedings{zpr97-265a, author = "S. P. Fekete and J. Schepers", institution = mi, title = "New classes of lower bounds for bin packing problems", journal = "submitted to: Mathematical Programming", year = "1998", crindex = "68k,11,zpr97-265a.ps.gz", keywords = "packing, bin packing, exact algorithm, lower bounds; 90C27, 68R99", annote = "The bin packing problem is one of the classical NP-hard optimization problems. Even though there are many excellent theoretical results, including polynomial approximation schemes, there is still a lack of methods that are able to solve practical instances optimally. In this paper, we present a fast and simple generic approach for obtaining new lower bounds, based on dual feasible functions. Worst case analysis as well as computational results show that one of our classes clearly outperforms the currently best known ``cheap'' lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. This indicates the usefulness of our results in a branch-and-bound framework.", } @InProceedings{zpr97-265, author = "S. P. Fekete and J. Schepers", institution = mi, title = "New classes of lower bounds for bin packing problems", booktitle = "Integer Programming and Combinatorial Optimization, Proc. 6th International IPCO Conference", location = "Houston, Texas", month = jun, year = "1998", editor = "R. E. Bixby and E. A. Boyd and R. Z. Ríos-Mercado", publisher = "Springer-Verlag", volume = "1412", series = "Lecture Notes in Computer Science", pages = "257--270", crindex = "68k,11,zpr97-265.ps.gz", keywords = "packing, bin packing, exact algorithm, lower bounds; 90C27, 68R99", annote = "The bin packing problem is one of the classical NP-hard optimization problems. Even though there are many excellent theoretical results, including polynomial approximation schemes, there is still a lack of methods that are able to solve practical instances optimally. In this paper, we present a fast and simple generic approach for obtaining new lower bounds, based on dual feasible functions. Worst case analysis as well as computational results show that one of our classes clearly outperforms the currently best known ``cheap'' lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. This indicates the usefulness of our results in a branch-and-bound framework.", } @Article{zpr97-264, author = "F. J. Brandenburg and M. J{\"u}nger and P. Mutzel", institution = inf, title = "Algorithmen zum automatischen Zeichnen von Graphen", journal = "Informatik-Spektrum", volume = "20", number = "4", pages = "199--207", month = aug, year = "1997", crindex = "131k,9,zpr97-264.ps.gz", keywords = "Automatic Graph Drawing, Planarization, Algorithms, Crossing Minimization, Graph Editors; 05C85, 90C", annote = "Graph drawing is a new and growing area in Computer Science. It is concerned with the design, analysis, implementation and evaluation of new algorithms for aesthetically nice drawings of graphs. Through the use of some selected examples of applications, typical problems, and solutions, we would like to provide an introduction into this still relatively unknown field. And we survey activities and goals of a working group consisting of members of the universities of Halle, K{\"o}ln and Passau and the Max-Planck-Institut f{\"u}r Informatik in Saarbr{\"u}cken, that is funded by the German Science Foundation DFG under the program `Efficient Algorithms for Discrete Problems and their Applications'.", } @Article{zpr97-263, author = "M. J{\"u}nger and S. Thienel", institution = inf, title = "Introduction to {ABACUS} - {A} Branch-and-{CU}t System", journal = "Operations Research Letters", volume = "22", number = "2--3", pages = "83--95", year = "1998", crindex = "51k,13,zpr97-263.ps.gz", keywords = "Mixed Integer Programming, Branch-and-Cut, Branch-and-Price, Software Systems; 90C10, 90C11, 90C27", annote = "The software system ABACUS is an object-oriented framework for the implementation of branch-and-cut and branch-and-price algorithms. This paper shows the basics of its application to combinatorial and mixed integer optimization problems.", } @InProceedings{zpr97-262, author = "P. Heusch and F. Meisgen and E. Speckenmeyer", institution = inf, title = "{CATS} - Computer Aided Tram Scheduling", booktitle = "To appear in: Proceedings of SOR '97", year = "1997", crindex = "52k,7,zpr97-262.ps.gz", keywords = "traffic simulation, combinatorial optimization, scheduling; 65C99, 68U20, 90C27", annote = "If public transport systems circulate periodically (e.g. 4 times per hour), their timetable is completely determined by the timetable for a single period, the so-called initial timetable. The initial timetable can then be used to calculate the other schedules, mainly those for vehicles and those for crews.
In our project CATS we deal with the computer aided construction and optimization of initial timetables. We currently develop a tool that allows for a simple user interface, very similar to the normally used paper-based user interface, which eases the task of construction while at the same time the developed plan is checked against the set of constraints. The data is stored in a database to facilitate the communication between timetable construction and the following steps.", } @Article{zpr97-261, author = "F. Meisgen and E. Speckenmeyer", institution = inf, title = "Dynamic Load Balancing on Clusters of Heterogenous Workstations", journal = "submitted to: Euro-Par '97, University of Passau, Germany", year = "1997", crindex = "62k,13,zpr97-261.ps.gz", keywords = "dynamic load balancing, workstation cluster, heterogenous system, parallel search algorithm, satisfiability problem; 68Q22, 90C27", annote = "When using the computing resources of workstation networks by parallel programs dynamic load balancing is an important task. We describe a distributed, local migration algorithm, called precomputation-based load balancing, which treats this problem efficiently. Its performance is empirically demonstrated solving the satisfiability problem on an heterogenous network of 12 workstations. We discuss the influence of processor weighting and parameter adaption on speedup and idle times.", } @TechReport{zpr97-260, author = "M. J{\"u}nger and S. Thienel", institution = inf, title = "The Design of the Branch-and-Cut System {ABACUS}", year = "1997", crindex = "99k,30,zpr97-260.ps.gz", keywords = "Mixed Integer Programming, Branch-and-Cut, Branch-and-Price, Software Systems; 90C10, 90C11, 90C27", annote = "The software system ABACUS is an object-oriented framework for the implementation of branch-and-cut and branch-and-price algorithms. This paper describes the design of ABACUS including the design principles and the most important classes.", } @TechReport{zpr97-259, author = "S. Leipert", institution = inf, title = "{PQ}-Trees, An Implementation as Template Class in {C}++", year = "1997", crindex = "265k,226,zpr97-259.ps.gz", keywords = "PQ-trees, data structure, software development; 68N, 68P05", annote = "PQ-trees are a data structure being used to represent the permutations of a set U in which various subsets of U occur consecutively. Along with the data structure, efficient algorithms for manipulating PQ-trees are given, requiring linear time in the size of the input. An implementation of the PQ-trees as template class allows easy checking of the consecutive ones property, without letting the user worry about the details of the algorithm. More sophisticated algorithms as planarity testing and embedding, computing planar subgraphs or finding cuts in the TSP, require the manipulation of the data structure. Therefore an implementation of the PQ-trees has to support possible manipulations of the data structure. This makes the implementation of the data structure reusable and allows the user a fast adaption to other implementations.", } @InProceedings{zpr97-258, author = "J. Schepers", institution = mi, title = "An Exact Algorithm for General Orthogonal n-dimensional Knapsack Problems", booktitle = "Operations Research Proceedings", editor = "U. Zimmermann and U. Derigs and W. Gaul and R. M{\"o}hring and K.-P. Schuster", publisher = "Springer-Verlag", year = "1997", crindex = "44k,7,zpr97-258.ps.gz", keywords = "orthogonal knapsack problem, two-dimensional cutting stock problem, 3-dimensional packing, exact algorithm, interval graph; 05C90, 90B06, 90C27, 90C28, 90C35", annote = "The n-dimensional orthogonal knapsack problem has a wide range of practical applications, including packing, cutting and scheduling. We present a new approach for its exact solution using a two-level tree search algorithm.
A key role plays a graph-theoretical characterization of packing patterns that allows us to deal with classes of packing pattern that are symmetrical in a certain sense, instead of single ones. Computational results are reported for two-dimensional test problems from literature.", } @InProceedings{zpr97-257, author = "A. Bachem and S. P. Fekete and B. Knab and R. Schrader and I. Vannahme and I. Weber and R. Wegener and K. Weinbrecht and B. Wichern", institution = mi, booktitle = "Beitr{\"a}ge zum 7. Symposium Geld, Finanzwirtschaft, Banken und Versicherungen, Dezember 1996", editor = "C. Hipp and W. Eichhorn and W.-R. Heilmann", publisher = "Verlag Versicherungswirtschaft", title = "Analyse gro{\ss}er Datenmengen und Clusteralgorithmen im Bausparwesen", pages = "955--961", year = "1997", crindex = "34k,7,zpr97-257.ps.gz", keywords = "data analysis, cluster analysis, single link, complete link; 62-07, 90A09, 90A19, 90A20", annote = "Kollektivanalysen und darauf aufbauende Prognosen sind seit langem ein wichtiger Beitrag der Bausparmathematik zu Fragen der Liquidit{\"a}tsplanung, der Produktpflege und der Produktentwicklung. Im Rahmen einer Kooperation zwischen den Landesbausparkassen und dem Zentrum f{\"u}r Paralleles Rechnen wurden daher Bausparmodelle entwickelt, die der Analyse des Verhaltens der Bausparer und der Vorhersage ihres zuk{\"u}nftigen Verhaltens dienen. Eine Weiterentwicklung dieser Modellans{\"a}tze mit Hilfe der Clusteranalyse soll in diesem Beitrag vorgestellt werden.", } @Article{zpr97-256a, author = "S. P. Fekete", institution = mi, title = "On Simple Polygonalizations with Optimal Area", journal = "to appear: Discrete and Computational Geometry", year = "1997", crindex = "193k,31,zpr97-256a.ps.gz", keywords = "geometric optimization, area, simple polygon, point separation, complexity, approximation, Traveling Salesman Problem, Pick's theorem, grid point, polyhedra; 90C28, 68Q25", annote = "We discuss the problem of finding a simple polygonalization for a given set of vertices P that has optimal area. We show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P and prove that it is NP-complete to find a minimum weight polygon or a maximum weight polygon for a given vertex set, resulting in a proof of NP-completeness for the corresponding area optimization problems. This answers a generalization of a question stated by Suri in 1989. Finally, we turn to higher dimensions, where we prove that for 1<= k <=d, 2<=d, it is NP-hard determine the smallest possible total volume of the k-dimensional faces of a d-dimensional simple nondegenerate polyhedron with a given vertex set, answering a generalization of a question stated by O'Rourke in 1980.", } @TechReport{zpr97-256, author = "S. P. Fekete", institution = mi, title = "Area optimization of simple polygons", year = "1997", crindex = "171k,45,zpr97-256.ps.gz", keywords = "geometric optimization, area, simple polygon, point separation, complexity, approximation, Traveling Salesman Problem, Pick's theorem, grid point, polyhedra; 90C28, 68Q25", annote = "We discuss problems of optimizing the area of a simple polygon for a given set of vertices P and show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P. We prove that it is NP-complete to find a minimum weight polygon or a maximum weight polygon for a given vertex set, resulting in a proof of NP-completeness for the corresponding area optimization problems. This answers a generalization of a question stated by Suri in 1989. We give evidence that it is unlikely that the minimization problem can be approximated. For the maximiation problem, we show that we can find in optimal time O(n log n) a polygon of more than half the area AR(conv(P)) of the convex hull conv(P) of P, yielding a fast 1/2 approximation method for the problem. We demonstrate that it is NP-complete to decide whether there is a simple polygon of at least (2/3+eps)(AR(conv(P)). We also sketch an NP-hardness proof for the problem of finding a minimum-link searating polygon for two finite point sets in the plane. Finally, we turn to higher dimensions, where we prove that for 0n. On the other hand, we show by construction that n>=22. These are the best existing bounds. We also note that planar graphs and complete bipartite graphs Km,n are representable, but that the family of representable graphs is not closed under graph minors.", } @TechReport{zpr96-252, author = "T. Hruz", institution = mi, title = "Ill-posed problems in control of distributed parameter systems", year = "1996", } @TechReport{zpr96-251, author = "W. Hochst{\"a}ttler and J. Nesetril", institution = mi, title = "Farkas' Lemma and Morphism Duality", year = "1996", crindex = "49k,12,zpr96-251.ps.gz", keywords = "oriented matroids, strong map, homomorphism, duality; 05B35, 05C99, 18B99, 90C05", annote = "In this paper we investigate the class $NP \cap co$-$NP$ (or the class of problems permitting a good characterisation) from the point of view of morphisms of oriented matroids. We prove several morphism duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma.", } @Article{zpr96-250a, author = "T. Christof and M. J{\"u}nger and J. Kececioglu and P. Mutzel and G. Reinelt", institution = inf, title = "A branch-and-cut approach to physical mapping with end-probes", journal = "Journal of Computational Biology", volume = "4", number = "4", pages = "433--447", year = "1997", crindex = "65k,9,zpr96-250.ps.gz", keywords = "computational biology, physical mapping of chromosomes, betweenness problem, linear ordering, branch-and-cut;", annote = "A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 52-76, 1995) first considered a maximum-likelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics.
We show that by exploiting information about the end-probes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the well-developed tools of integer linear-programming and branch-and-cut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively screen errors from larger instances, and solve the edited instance to optimality as a Hamming-Distance Traveling Salesman Problem. This suggests a new combined approach to physical map construction.", } @InProceedings{zpr96-250, author = "T. Christof and M. J{\"u}nger and J. Kececioglu and P. Mutzel and G. Reinelt", institution = inf, title = "A branch-and-cut approach to physical mapping with end-probes", booktitle = "Proceedings of the First International Conference on Computational Molecular Biology (RECOMB-1), Santa Fe, New Mexico, 1997", publisher = "ACM Press", pages = "84--92", year = "1997", crindex = "65k,9,zpr96-250.ps.gz", keywords = "computational biology, physical mapping of chromosomes, betweenness problem, linear ordering, branch-and-cut;", annote = "A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 52-76, 1995) first considered a maximum-likelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors, and developed several effective heuristics.
We show that by exploiting information about the end-probes of clones, this model can be formulated as a weighted Betweenness Problem. This affords the significant advantage of allowing the well-developed tools of integer linear-programming and branch-and-cut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively screen errors from larger instances, and solve the edited instance to optimality as a Hamming-Distance Traveling Salesman Problem. This suggests a new combined approach to physical map construction.", } @TechReport{zpr96-249, author = "W. Hochst{\"a}ttler and M. Laurent and M. Loebl", institution = mi, title = "Cycle bases for lattices of matroids with no Fano dual minor and their one-element extensions", year = "1996", crindex = "78k,16,zpr96-249.ps.gz", keywords = "geometry of numbers, binary matroids, lattice basis; 05B40, 11H31, 52C17", annote = "In this paper we study the question of existence of a basis consisting only of cycles for the lattice Z(M) generated by the cycles of a binary matroid M. We show that, if M has no Fano dual minor, then any set of fundamental circuits can be completed to a cycle basis of Z(M); moreover, for any one-element extension M of such matroid M, any cycle basis for Z(M) can be completed to a cycle basis for Z(M).", } @Article{zpr96-248, author = "R. Schrader and G. Wambach", institution = inf, title = "The setup polytope of {N}-sparse posets", journal = "Annals of Operations Research", volume = "92", pages = "125--142", publisher = "Baltzer", location = "Basel", year = "1999", annote = "The setup problem is the following single-machine scheduling problem: There are n jobs with individual processing times, arbitrary precedence relations and sequence-dependent setup costs (or changeover times). The setup cost sef arises in a schedule if job f is processed immediately after job e, e.g., the machine must be cleaned of e and prepared for f. The goal is to find a schedule minimizing the total setup costs (and thus, for changeover times, the makespan). We consider the case of ''precedence-induced`` setup costs where a nonzero term sef occurs only if e and f are unrelated with respect to the precedence relations. Moreover, we assume that the setup costs depend only on f, i.e., sef = sf for all e which are unrelated to f.
Two special cases of the setup problem with precedence-induced setup costs are the jump numberproblem and the bump number problem. We suggest a new polyhedral model for the precedence-induced setup problem. To every linear extension L = e1 e2 en ... of a poset P = (P1 <) with n elements, we associate a 0, 1-vector xL \in RP with xeL = 1 if and only if e starts a chain in L (e = e1 or e = ei+1 | ei ). The setup polytope S is the convex hull of the incidence vectors of all linear extensions of P. For N-sparse posets P, i.e., posets whose comparability graph is P4-sparse, we give a complete linear description of S. The integrality part of the proof employs the concept of box total dual integrality.", } @TechReport{zpr96-247, author = "O. Bastert and S. P. Fekete", institution = mi, title = "Geometrische Verdrahtungsprobleme", year = "1996", crindex = "321k,81,zpr96-247.ps.gz", keywords = "geometric optimization, VLSI design, complexity, lower bounds; 68Q35, 68U05, 90C28", annote = "We consider the problem of connecting n pairs of points in the plane by pairwise disjoint geometric paths (``wires''). This problem is closely related to geometric aspects of chip layout; the question of the existence of a set of pairwise disjoint connections has been studied widely. In a purely geometric setting, there always is a set of disjoint wires, so the main issue is to optimize the layout. We consider several objective functions involving the length as well as the number of bends of the wires.
We present techniques for showing NP-hardness of this type of geometric problem. Furthermore, we prove a lower bound for the number of bends that may be necessary. Finally, we discuss approximation methods.", } @TechReport{zpr96-246, author = "J. Geelen", institution = mi, title = "Lectures on Jump Systems", year = "1996", crindex = "69k,20,zpr96-246.ps.gz", keywords = "matching, matroids, combinatorial optimization; 05C70, 05B35", annote = "A jump system is a nonempty set of integral vectors that satisfy a certain exchange axiom. This notion was introduced by Bouchet and Cunningham, and popularized by recent results of Lovász. A degree system of a graph G is the set of degree sequences of all subgraphs of G. Degree systems are the primary example of jump systems. Other examples come from matroids and from two generalizations of matroids (polymatroids and delta-matroids). Discussion of these special cases will be kept to a minimum, and will only be used to motivate certain results.
The main result is a min-max formula of Lovász for the distance of an integral point from a jump system. This formula generalizes two of the more important min-max theorems in combinatorial optimization; namely, Tutte's f-factor-theorem, and Edmonds' matroid intersection theorem. Other points of interest are the existence of a greedy algorithm for optimizing linear functions, and a characterization of the convex hulls of jump systems. Even apart from the possibility of obtaining very general theorems, jump systems are appealing due to their simple definition and elegant structure.", } @TechReport{zpr96-245, author = "S. Thienel", institution = inf, title = "A Simple {TSP}-Solver: An {ABACUS} Tutorial", year = "1996", crindex = "102k,34,zpr96-245.ps.gz", keywords = "traveling salesman problem, mixed integer programming; 68-04, 90C11, 90C27", annote = "This CWEB program shows how a branch-and-cut algorithm for the traveling salesman problem (TSP) can be implemented with the software framework ABACUS. The intention of this program is not the practically efficient solution of TSPs but to show basic and some advanced features of ABACUS.", } @TechReport{zpr96-244, author = "S. Thienel", institution = inf, title = "{ABACUS} - {A} Branch-And-{CU}t System, Version 1.2, User's Guide and Reference Manual", year = "1996", keywords = "combinatorial optimization, mixed integer programming, branch-and-cut; 68-04, 90C11, 90C27", annote = "ABACUS is a C++ framework for the implementation of branch-and-cut algorithms, branch-and-price algorithms, and their combination for linear mixed integer and combinatorial optimization problems. This manual explains the installation, the design, and the usage of the framework. Both the basic steps and advanced features are discussed. The reference manual describes all classes together with all members that are relevant for the user.
See Report No. 298 for Version 2.0.", } @Article{zpr96-243, author = "M. J{\"u}nger and P. Mutzel", institution = inf, title = "2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms", journal = "Journal of Graph Algorithms and Applications", volume = "1", number = "1", pages = "1--25", year = "1997", crindex = "115k,14,zpr96-243.ps.gz", keywords = "Automatic Graph Drawing, Crossing Minimization, Linear Ordering, Polyhedral Combinatorics, branch-and-cut; 05C99, 68R99", annote = "We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NP-hard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes. For bigger instances, the iterated barycenter method turns out to be the method of choice among several popular heuristics whose performance we could assess by comparing the results to optimum solutions.", } @TechReport{zpr96-242, author = "S. Leipert", institution = inf, title = "The Tree Interface -- Version 1.0 User Manual", year = "1996", crindex = "168k,53,zpr96-242.ps.gz", keywords = "Graphical Interface, Software Development, Graph Drawing; 90C, 68N", annote = "The Tree Interface is a graphical tool specially designed to draw binary and general rooted trees, as they occur during an algorithmic process. It can be used in three different contexts.
The Tree Interface provides all necessary features of a graphical interface, such as area zoom, mouse dragging, print command and a colour, font and size chooser. The software has been compiled for SunOS, Solaris and Linux and is available under the following address: http://www.informatik.uni-koeln.de/ls_juenger/projects/vbctool.html ", } @TechReport{zpr96-241, author = "M. J{\"u}nger and V. Kaibel", institution = inf, title = "On the {SQAP}-Polytope", year = "1996", crindex = "127k,28,zpr96-241.ps.gz", keywords = "Symmetric Quadratic Assignment Problem, polyhedral combinatorics, SQAP-Polytope; 90C09, 90C10, 90C27", annote = "The study of the QAP-Polytope was started by Rijal (1995), Padberg and Rijal (1996), and J{\"u}nger and Kaibel (1996), investigating the structure of the feasible points of a (Mixed) Integer Linear Programming formulation of the QAP that provides good lower bounds by its continious relaxation.
Rijal (1995), Padberg and Rijal (1996) propose an alternative (Mixed) Integer Linear Programming formulation for the case that the QAP-instance is symmetric in a certain sense and define analogously the SQAP-Polytope. They give a conjecture about the dimension of that polytope, whose proof is one part of this paper. Moreover, we investigate the trivial faces of the SQAP-Polytope and present a first class of non-trivial facets of it. The polyhedral results are used to compute lower bounds for symmetric QAPs.", } @TechReport{zpr96-240, author = "F. Damm and F.-P. Heider", institution = inf, title = "Amplifying the Security of One-Way Functions -- {A} Proof of Yao's {XOR}-Lemma", year = "1996", crindex = "57k,13,zpr96-240.ps.gz", keywords = "computational complexity, cryptography, theory of computation, one-way functions; 94A60, 68P25, 68Q15, 68Q25", annote = "In this paper we give a consistent and simple proof for the XOR-Lemma which was hinted at by Yao and subsequently presented by him in lectures. It can be found in print in E. Kranakis, Primality and Cryptography, Wiley-Teubner Series in Computer Science, 1986.
By the lemma we know that the security of any one-way function $f:X\longrightarrow \{ 0,1\}$ can be substantially amplified if the function is replaced by the XOR with itself, namely by $f\oplus f:X\times X\longrightarrow \{ 0,1\}, (x,y)\longrightarrow f(x)\oplus f(y)$.
Applications are in cryptography and complexity theory. However, the existence of one-way functions still remains an open problem.", } @InProceedings{zpr96-239, author = "A. Hamacher and C. Moll", institution = mi, title = "A New Heuristic for Vehicle Routing with Narrow Time Windows", booktitle = "Operations Research Proceedings 1996. Selected papers of the symposium, SOR'96, Braunschweig, Germany, September 3-6, 1996", editor = "U. Zimmermann and U. Derigs and W. Gaul and R. M{\"o}hring and K.-P. Schuster", publisher = "Springer-Verlag", year = "1996", pages = "301--306", crindex = "52k,11,zpr96-239.ps.gz", keywords = "vehicle routing, time windows, tree partition, minimal spanning tree, greedy algorithm; 05C05, 05C85, 05C90, 68R10, 90B06, 90C27, 90C35", annote = "This paper describes a new heuristic for vehicle routing problems with narrow time windows. The problem arises in the context of the delivery of groceries to restaurants. For most of the instances the given time window distribution does not allow solutions where no time restrictions are violated. The aim is to schedule most of the customers in time building regionally bounded tours. The few remaining customers have to be scheduled manually. If the disponent decides to serve one or more of the remaining customers in time, he has to allow out-of-time deliveries for some of the automatically planned stops. The algorithm is based on a clustering procedure where a tree with multiple node weights is divided into subtrees. Upper bounds restrict the sums of the weight functions in each subtree. This problem is NP-complete even for trees with bounded degree and more than two weight functions. A greedy algorithm is developed to determine the tree partition. For our application it is extended to a version which also checks if each subtree can be routed regarding the problem specific requirements. Although the algorithm was developed for a specific real world problem, the ideas can also be applied to other vehicle routing problems - even to those with more complicated constraints.", } @Article{zpr96-238, author = "P. Wagner and K. Nagel and D. E. Wolf", institution = mi, title = "Realistic Multi--Lane Traffic Rules for Cellular Automata", journal = "Physica A", volume = "234", pages = "687--698", year = "1996", crindex = "59k,12,zpr96-238.ps.gz", keywords = "traffic simulation, cellular automata,lane changing; 65C20, 90B20, 60J20, 82C22, 82B41", annote = "A set of lane changing rules for cellular automata simulating multi-lane traffic is proposed. It reproduces qualitatively that the passing lane becomes more crowded than the one for slower cars if the flux is high enough, which is true for motorways in countries like Germany where passing should be done on a specified lane as a rule. The rules have two parameters allowing to adjust the inversion point of the lane usage distribution and to calibrate the model.", } @PhdThesis{zpr96-237, author = "I. Vannahme", school = mi, title = "Clusteralgorithmen zur mathematischen Simulation von Bausparkollektiven", year = "1996", crindex = "523k,165,zpr96-237.ps.gz", keywords = "cluster analysis, single link, complete link, k-means; 62-07, 90A09, 90A19, 90A20", annote = "Seit den Anf{\"a}ngen der Bausparmathematik in den 20er Jahren steht die Entwicklung von mathematischen Modellen zur Prognose der Ertrags- und Liquidit{\"a}tslage im Vordergrund. W{\"a}hrend zu Beginn nur einfache mathematische Modelle genutzt wurden, die auf einfachen Einzelvertragsabl{\"a}ufen basierten, sind in den letzten 20 Jahren wesentlich komplexere Simulationsmodelle entwickelt worden. Dies ist vor allen Dingen darauf zur{\"u}ckzuf{\"u}hren, da{\ss} die Prognose der wirtschaftlichen Entwicklung von Bausparkollektiven vor dem Hintergrund der sich {\"a}ndernden gesetzlichen Auflagen und dem st{\"a}rker werdenden Konkurrenzkampf unter den Bausparkassen zunehmende Bedeutung gewinnt. Die {\"a}lteren einfachen Modelle reichen heute kaum aus, die komplexen Gestaltungsm{\"o}glichkeiten in den einzelnen Tarifen abzubilden. Auch Gesetzes{\"a}nderungen, wie der 1990 eingef\{\"u}hrte Fonds zur bauspartechnischen Sicherung, erfordern eine genauere Planung durch die Bausparkassen.
Am Mathematischen Institut der Universit{\"a}t zu K{\"o}ln werden in Zusammenarbeit mit der Gruppe der Landesbausparkassen Modelle zur Simulation von Bausparkollektiven entwickelt. Im Rahmen dieser Zusammenarbeit ist auch das mathematische Simulationsmodell entstanden, das in dieser Arbeit vorgestellt wird. Dieses Modell wurde aus einem bestehenden Modell mit neuen Methoden mit dem Ziel entwickelt, eine Verbesserung der Prognosequalit{\"a}t durch die Verwendung moderner Clusterverfahren zu erreichen.
Die Arbeit gliedert sich in einen bauspartechnischen und einen mathematischen Teil.
Im bauspartechnischen Teil wird zum Verst{\"a}ndnis der Thematik des Bausparens und der Aufgabenstellung zu Beginn eine allgemeine Einf{\"u}hrung in die Entwicklung des Bausparens gegeben. Weiterhin werden die technischen Merkmale, die bei der Modellierung des Bauspargeschehens abzubilden sind, erl{\"a}utert, um darauf aufbauend mittels eines einfachen Vertragsablaufs ein Gesamtmodell zu entwickeln. Nach einem {\"U}berblick {\"u}ber die historische Entwicklung von Simulationsmodellen f{\"u}r Bausparkollektive werden zwei Modellans{\"a}tze, ein {\"o}konometrischer Ansatz und ein Schichtenmodell, genauer vorgestellt. Das in dieser Arbeit besonders wichtige Mikrosimulationsmodell wird in einem eigenen Kapitel erl{\"a}utert.
Im mathematischen Teil betrachten wir die Problematik der Clusterung. In einem ersten Abschnitt wird zun{\"a}chst die Definition verschiedener Clusterprobleme behandelt. Dabei steht die mathematische Komplexit{\"a}t der verschiedenen Probleme im Vordergrund. Anschlie{\ss}end werden L{\"o}sungsverfahren f{\"u}r einige ausgew{\"a}hlte Clusterprobleme vorgestellt. In einem weiteren Teil wird auf die Problematik der Abstandsma{\ss}e eingegangen. Ein wichtiges Problem der Clusteranalyse ist die Bewertung der gefundenen Gruppierung, wobei die Qualit{\"a}t einer Clusterung im wesentlichen von der Zielsetzung abh{\"a}ngt. Es stehen aber auch mathematische G{\"u}tekriterien zur Beurteilung einer Clusterung zur Verf{\"u}gung, von denen insbesondere auch f{\"u}r gro{\ss}e Datenmengen geeignete in einem abschlie{\ss}enden Abschnitt behandelt werden.
Im letzten Teil der Arbeit wird die Nutzbarkeit von Clusterverfahren zur Steuerung eines Prognosemodells f{\"u}r Bausparkollektive erl{\"a}utert. Zun{\"a}chst wird ein Abstandsma{\ss} entwickelt, das die wichtigsten Merkmale eines Bausparvertrags ber{\"u}cksichtigt. Mit diesem Abstandsma{\ss} werden verschiedene Clusterverfahren bez{\"u}glich ihrer Eignung f{\"u}r die Clusterung von Bausparvertr{\"a}gen untersucht. Die Ergebnisse der verschiedenen Clusterungen werden mit Hilfe der im vorangegangenen Abschnitt vorgestellten G{\"u}tekriterien verglichen, und mit einem besonders geeigneten Verfahren werden abschlie{\ss}end Prognosen durchgef{\"u}hrt. Es kann gezeigt werden, da{\ss} die Nutzung von Clusterverfahren die Prognose gegen{\"u}ber dem zuvor verwendeten Rasterverfahren verbessert.
In der Arbeit werden alle ben{\"o}tigten Grundlagen kurz zusammengefa{\ss}t. Um die Lesbarkeit zu erh{\"o}hen, befinden sich die graphentheoretischen und komplexit{\"a}tstheoretischen Grundbegriffe in Anhang\ \ref{graph} bzw.\ \ref{kompl_anh}. Im Anhang\ \ref{bauspar} wird auf die unterschiedlichen Gestaltungsm{\"o}glichkeiten eines Bausparvertrags eingegangen. Ebenfalls im Anhang findet sich ein {\"U}berblick {\"u}ber die gesetzlichen Grundlagen des Bausparens in Deutschland.", } @InProceedings{zpr96-236, author = "M. Strietzel", institution = mi, title = "Parallel Turbulence Simulation based on {MPI}", booktitle = "High Performance Computing and Networking", editor = "H. M. Liddell and A. Colbrook and B. Hertzberger and P. Sloot", note = "International Conference and Exhibition, Brussels, Belgium, April 1996, Proceedings", publisher = "Springer-Verlag", volume = "1067", series = "Lecture Notes in Computer Science", pages = "283--289", year = "1996", crindex = "88k,6,zpr96-236.ps.gz", keywords = "Parallel computing, Navier-Stokes equation, turbulence simulation, Poisson equation; 35Q30,76F05", annote = "We describe a parallel implementation for large-eddy simulation and direct numerical simulation of turbulent fluids based on the three dimensional incompressible Navier-Stokes equation. The parallelization strategy is specified by domain decomposition and a divide and conquer method for solving the poisson equation. The program is benchmarked on a set of supercomputers under the message passing platform MPI. Running times of these tests are presented.", } @InCollection{zpr96-235, author = "E. Speckenmeyer and M. B{\"o}hm and P. Heusch", institution = inf, title = "On the Imbalance of Distributions of Solutions of {CNF}-Formulas and its Impact on Satisfiability Solvers", booktitle = "Satisfiability Problem: Theory and Applications", series = "DIMACS Series in discrete mathematics and theoretical computer science", editor = "D. Du and J. Gu and P. M. Pardalos", volume = "35", pages = "669--676", year = "1997", crindex = "76k,11,zpr96-235.ps.gz", keywords = "satisfiability solving, distribution of solutions; 68Q22, 68Q25,68T20", annote = "Let F be Boolean formulas in conjunctive normal form with n variables, r clauses, every clause has length s. We show that if F is split into two subformulas $F_{v}$ and $F_{\overline{v}}$ by setting v true and false in F, then the expected number of solutions of one of the two subformulas $F_{v}$ and $F_{\overline{v}}$ is significantly higher than that in the other subformula, when dealing with classes of formulas where the great majority of formulas is satisfiable. We discuss practical consequences of this result.", } @InProceedings{zpr96-234, author = "A. Bachem and B. Monien and H. J. Pr{\"o}mel and R. Schrader and B. Voigt", booktitle = "Stand und Perspektiven des Parallelen H{\"o}chstleistungsrechnens und seiner Anwendungen", note = "Beitrag zur Statustagung des BMBF, IIPSC 95", title = "Verbundprojekt {PARALOR}: Parallele Algorithmen f{\"u}r Routingprobleme im Flug- und Stra{\ss}enverkehr", year = "1996", crindex = "131k,19,zpr96-234.ps.gz", keywords = "parallel algorithms, fleet assignment, crew scheduling, vehicle routing, 3-dimensional packing, branch-and-bound, simulated trading; 90B06, 90B35, 90C08", annote = "Im Verbundprojekt PARALOR wird untersucht, wie parallele Algorithmen der kombinatorischen Optimierung zur L{\"o}sung gro{\ss}er Optimierungsprobleme aus der industriellen Praxis eingesetzt werden k{\"o}nnen. Dabei werden insbesondere konkrete Aufgabenstellungen aus dem Bereich der Flugplanoptimierung und der integrierten Steuerung von Fertigungslagern bearbeitet. Der Beitrag gibt einen {\"U}berblick {\"u}ber die jeweiligen Problemstellungen, die verwendeten Algorithmen und die bisher erzielten Resultate. Insbesondere werden mit dem Parallelen Simulated Trading und dem Parallelen Branch-and-Bound parallele Methoden betrachtet, mit denen eine breite Klasse kombinatorischer Optimierungsprobleme behandelt werden kann.", } @Article{zpr96-233, author = "E. Knill and A. Schliep and D. Torney", institution = mi, journal = "Journal of Computational Biology", volume = "3", number = "3", pages = "395--406", title = "Interpretation of Pooling Experiments Using the Markov Chain Monte Carlo Method", year = "1996", crindex = "63k,21,zpr96-233.ps.gz", keywords = "Markov Chains, monte carlo method, clone libraries, pooling; 62M05, 92D20", annote = "This paper describes an effective method for extracting as much information as possible from pooling experiments for library screening. Pools are collections of clones, and screening a pool with a probe is a group test, determining whether any of these clones are positive for the probe.
The results of the pool screenings are interpreted, or decoded, to infer which clones are candidates to be positive. These candidate positives are subjected to confirmatory testing. Decoding the pool screening results is complicated by the presence of errors, which typically lead to ambiguities in the inference of positive clones. However, in many applications there are reasonable models for the prior distributions for positives and for errors, and Bayes inference is the preferred method for ranking candidate positives.
Because of the combinatoric complexity of the Bayes formulation, we implemented a decoding algorithm using a Markov chain Monte Carlo method. The algorithm was used in screening a library with 1298 clones using 47 pools. We corroborated the posterior probabilities for positives with results from confirmatory screening. We also simulated the screening of a tenfold-coverage library of 33,000 clones using 253 pools. The use of our algorithm, effective under conditions where combinatorial decoding techniques are imprudent, allows the use of fewer pools and also introduces needed robustness.", } @Article{zpr96-232, author = "U. Blasum and M. Bussieck and W. Hochst{\"a}ttler and C. Moll and H. Scheel and T. Winter", institution = mi, title = "Scheduling Trams in the Morning", journal = "Mathematical Methods of Operations Research", volume = "49", number = "1", year = "1999", pages = "137--148", crindex = "57k,10,zpr96-232.ps.gz", keywords = "combinatorial optimization, complexity, NP-completeness, scheduling, assignment; 90C60,90C27,68Q25", annote = "In this note, we prove NP-completeness of the following problem: Given a set of trams of different types, which are stacked on sidings in their depot and an order in which trams of specified types are supposed to leave. Is there an assignment of trams to departure times without any shunting movements? For the special case where the number of sidings is fixed the problem is solvable in polynomial time. We derive a brute force and a more sophisticated implementation of the associated algorithm. Furthermore, we compare the implementations on random and real word data.", } @Article{zpr96-231, author = "H. Rieger and L. Santen and U. Blasum and M. Diehl and M. J{\"u}nger and G. Rinaldi", institution = inf, title = "The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations", journal = "Journal of Physics A: Mathematical and General", volume = "29", number = "14", pages = "3939--3950", month = jul, year = "1996", crindex = "136k,8,zpr96-231.ps.gz", keywords = "spin glasses, branch-and-cut, critical exponents, monte carlo method; 82D30, 90C", annote = "The critical exponents for T -> 0 of the two-dimensional Ising spin glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to L=50 and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent $y(=\theta)=-0.281 ±0.002$, for the magnetic exponent $\delta=1.48 ±0.01$ and for the chaos exponent $\zeta=1.05 ±0.05$. From Monte Carlo simulations we get the thermal exponent $\nu=3.6 ±0.2$. The scaling prediction $y=-1/\nu$ is fulfilled within the error bars, whereas there is a disagreement with the relation $y=1-\delta$.", } @TechReport{zpr96-230, author = "J. Franco and G. Gallo and H. Kleine B{\"u}ning and E. Speckenmeyer and C. Spera", institution = inf, title = "Workshop on the Satisfiability problem", location = "Siena, Italy", year = "1996", keywords = "satisfiability problem,satisfiability solving, algorithms, data structure, complexity logic,programming, propositional logic, NP-completeness, combinatorial optimization, resolution; 03B, 68T", annote = "
Reactive Search: A History-Based Heuristic for MAX-SAT
R. Battiti and M. Protasi
Abstract: ps

On Satisfiability of Partially Defined Double and Bidual Horn Functions
T. Eiter, T. Ibaraki and K. Makino
Paper: ps

An Algorithm for the Class of Pure Implicational Formulas
J. Franco, J. Goldsmith, J. Schlipf, E. Speckenmeyer and R. P. Swaminathan
Abstract: ps

Max Horn SAT and Directed Hypergraphs: Algorithmic Enhancements and Easy Cases
G. Gallo, C. Gentile and D. Pretolani
Paper: ps

Lemma and Cut Strategies for Two-Sided Propositional Resolution
A. Van Gelder and F. Kamiya
Paper: ps

Probability of Satisfiability of Random 2-SAT Instances with Quantification
A. Goerdt
Abstract: ps

Complexity Results of Subclasses of the Pure Implicational Calculus
P. Heusch, M.-A. Lemburg and E. Speckenmeyer
Paper: ps

Closure under Replacements Versus Run Time of Davis-Putnam Algorithms and Distribution of satisfiable Formulas
H. Kleine Büning and T. Lettmann
Paper: ps

Resolution remains Hard under Equivalence
H. Kleine Büning and T. Lettmann
Paper: ps

A Note on a Generalization of Extended Resolution
O. Kullmann
Paper: ps

Elliptic Approximations of Propositional Formulae
H. van Maaren
Paper: ps

Toward an Adequate SAT Algorithm
D. Mitchell and H. Levesque
Abstract: ps

Strengthening Lagrangian Bounds for the MAX-SAT Problem
P. Nobili and A. Sassano
Paper: ps

Probe Order Backtracking
P. Purdom
Abstract: ps

Pure Literal Look Ahead: An O(1,497n) 3-Satisfiability Algorithm
I. Schiermeyer
Paper: ps

The Symmetry Rule in Propositional Logic
A. Urquhart
Paper: ps

Back-Positioning in SAT Searching
J. Wang
Paper: ps

Schedule ps

List of Participants ps

Table of Contents ps

", } @Article{zpr96-229, author = "C. De Simone and M. J{\"u}nger", institution = inf, title = "On the Two-Connected Planar Spanning Subgraph Polytope", journal = "Discrete Applied Mathematics", volume = "80", number = "2-3", pages = "223--229", year = "1997", crindex = "50k,7,zpr96-229.ps.gz", keywords = "planar graphs, two-connected graphs, polyhedra, facets; 05C10", annote = "The problem of finding in a complete edge-weighted graph a two-connected planar spanning subgraph of maximum weight is important in automatic graph drawing. We investigate the problem from a polyhedral point of view.", } @TechReport{zpr96-227, author = "M. J{\"u}nger and S. Leipert and P. Mutzel", institution = inf, title = "On Computing a Maximal Planar Subgraph using {PQ}-Trees", year = "1996", crindex = "111k, 12,zpr96-227.ps.gz", keywords = "PQ-Trees, maximal planar subgraphs, planarization; 05C85, 68R10, 90C35", annote = "The problem of computing a maximal planar subgraph of a non-planar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of PQ-trees. The latest attempt has been reported by Jayakumar, Thulasiraman and Swamy (1989).
In this paper we show that the algorithm presented by Jayakumar et al. is not correct. We show that it does not necessarily compute a maximal planar subgraph and that the same holds for a modified version of the algorithm presented by Kant (1992). Our conclusions most likely suggest not to use PQ-trees at all for this specific problem.", } @InProceedings{zpr96-226, author = "S. P. Fekete and W. Hochst{\"a}ttler and S. Kromberg and C. Moll", institution = mi, title = "The Complexity of an Inverse Shortest Path Problem", booktitle = "Contemporary Trends in Discrete Mathematics: From DIMACS and DIMATIA to the Future", series = "DIMACS Series in Discrete Mathematics and Theoretical Computer Science", volume = "49", editor = "R. L. Graham and J. Kratochvíl and J. Nesetril and F. S. Roberts", publisher = "AMS", year = "1999", crindex = "88k, 18,zpr96-226.ps.gz", keywords = "distance in graphs, planar graphs, shortest paths, inverse shortest paths, computational complexity, NP-completeness; 05C12, 68Q25", annote = "In this paper we study the complexity of an Inverse Shortest Paths Problem (ISPP). We show that this problem is intractable even in very restricted cases. In particular, we prove that this Inverse Shortest Paths Problem is NP-complete in the planar case. Furthermore, we give a characterization of the class of graphs Gd of given distances for which the ISPP is tractable: we give polynomial algorithms for special classes of Gd and provide evidence that no polynomial time algorithms exist if the structure of Gd is only slightly more complicated in a well-defined graph-theoretical sense. Finally, we discuss the situation for directed graphs.", } @Article{zpr96-225, author = "S. P. Fekete and G. J. Woeginger", institution = mi, journal = "Computational Geometry", title = "Angle-Restricted Tours in the Plane", pages = "195--218", volume = "8", number = "4", year = "1997", crindex = "160k,29,zpr96-225.ps.gz", keywords = "Angle-restrictions, computational complexity, convexity, geometry, Traveling Salesman Problem, Hamiltonian cycle, NP-complete; 51A20, 68R05, 68U05", annote = "For a given set $A \subseteq\ (-\pi;+\pi]$ of angles, the problem ``Angle-Restricted Tour'' (ART) is to decide whether a set P of n points in the Euclidean plane allows a closed directed tour consisting of straight line segments, such that all angles between consecutive line segments are from the set A.
We present a variety of combinatorial and algorithmic results on this problem. In particular, we show that any finite set of at least 5 points allows a ``pseudoconvex'' tour, where all angles are nonnegative.", } @Article{zpr96-224, author = "S. P. Fekete and H. Meijer", institution = mi, title = "Rectangle and Box Visibility Graphs in 3{D}", journal = "International Journal of Computational Geometry and Applications", year = "1999", volume = "9", number = "1", pages = "1--27", crindex = "91k,28,zpr96-224.ps.gz", keywords = "graph representation, visibility, graph drawing, 3-dimensional geometry; 05C10, 05C75, 68R05,68R10", annote = "We discuss rectangle and box visibility representations of graphs in 3-dimensional space. In these representations, vertices are represented by axis-aligned disjoint rectangles or boxes.
Two vertices are adjacent if and only if their corresponding boxes see each other along a small axis-parallel cylinder. We concentrate on lower and upper bounds for the size of the largest complete graph that can be represented. In particular, we examine these bounds under certain restrictions: What can be said if we may only use boxes of a limited number of shapes?
Some of the results presented are as follows:
There is a representation of K8 by unit boxes.
There is no representation of K10 by unit boxes.
There is a representation of K56, using 6 different box shapes.
There is no representation of K184 by general boxes.

A special case arises for rectangle visibility graphs, where no two boxes can see each other in the x- or y-directions, which means that the boxes have to see each other in z-parallel direction. This special case has been considered before; we give further results, dealing with the aspects arising from limits on the number of shapes.", } @TechReport{zpr96-223, author = "W. Hochst{\"a}ttler", institution = mi, title = "Semidefinite Programmierung", year = "1996", crindex = "162k,95,zpr96-223.ps.gz", keywords = "semidefinite programming, interior point methods, eigenvalue optimization, combinatorial optimization, maximum cliques, perfect graphs, graph partitioning; 90C10, 90C25, 90C27, 15A18, 68R10", annote = "Dies ist das Skriptum des zweiten Teils der Vorlesung {\"u}ber Nichtlineare Optimierung von Professor Dr. A.Bachem. Der erste Teil behandelte die Grundz{\"u}ge des Standardstoffs, wie er etwa in dem Buch von D. G. Luenberger, Introduction to Linear and Nonlinear Programming (Second Edition), Addison-Wesley Publishing Company, Reading 1984, vorgestellt wird. Wir hatten eine Zweiteilung der Vorlesung geplant, um in der zweiten H{\"a}lfte Stoff pr{\"a}sentieren zu k{\"o}nnen, der n{\"a}her an der aktuellen Forschung ist.
Dabei kam die Idee auf, semidefinite Programmierung zu besprechen. Da wir in diesem Gebiet selbst nicht arbeiten und die Inhalte noch zu neu sind, als da{\ss} bereits hinreichend Literatur f{\"u}r die Lehre existieren w{\"u}rde, entschlossen wir uns erst, als wir im Internet Skripten eines Kurses von Farid Alizadeh zu diesem Thema entdeckten, den zweiten Teil der Vorlesung mit diesen Inhalten zu bestreiten.
Mit dem Wechsel von Professor Dr. A. Bachem in den Vorstand der DLR habe ich die Aufarbeitung der Skripten und die Vorstellung des Stoffes in der Vorlesung {\"u}bernommen. Da es sich bei der Vorlage um einen Kurs handelt, der im Rahmen eines Ph.D. Programms abgehalten wurde, sind die Originalskripten manchmal etwas knapp gehalten. Deshalb m{\"o}chte ich den Zuh{\"o}rern unseres Kurses mit dieser deutschen Ausarbeitung der Vorlage weitere Literatur zur Verf{\"u}gung stellen.
Auch f{\"u}r einen Leser, der den ersten Teil der Vorlesung nicht geh{\"o}rt hat, sollte das Skriptum verst{\"a}ndlich sein. Die wenigen Stellen, an denen auf diesen Stoff Bezug genommen wird, sollten f{\"u}r ein Gesamtverst{\"a}ndnis nicht wesentlich sein. Die zugeh{\"o}rigen Zusammenh{\"a}nge kann man in verschiedenen Standardwerken nachlesen.", } @Article{zpr96-222, author = "U. Blasum and W. Hochst{\"a}ttler and C. Moll and H. Rieger", institution = mi, title = "Using network-flow techniques to solve an optimization problem from surface-physics", journal = "Journal of Physics A: Mathematical and General", volume = "29", number = "18", pages = "L459--L463", month = sep, year = "1996", crindex = "36k,7,zpr96-222.ps.gz", keywords = "crystal growth, network-flow, convex minimum circulation problem; 82D", annote = "The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.", } @Proceedings{zpr96-221, author = "P. Heusch and E. Speckenmeyer", institution = inf, title = "28. Workshop {\"u}ber Komplexit{\"a}tstheorie, Datenstrukturen und effiziente Algorithmen", year = "1996", series = "to appear in: Special Issue of Discrete Applied Mathematics", crindex = "66k,13,zpr96-221.ps.gz", annote = "Prof. Dr. Ewald Speckenmeyer, Dr. Peter Heusch
Institut f{\"u}r Informatik
Universit{\"a}t zu K{\"o}ln
D-50969 K{\"o}ln
Tel.: +49 221 470-5378
Fax: +49 221 470-5387

Programm des 28. Workshops {\"u}ber
Komplexit{\"a}tstheorie, Datenstrukturen und effiziente Algorithmen
am 27.02.96 im
H{\"o}rsaal des Pohlighauses der
Universit{\"a}t zu K{\"o}ln

09.25 Uhr Begr{\"u}{\"s}ung
09.30-09.55 Uhr U. Hertrampf, Trier:
{\"U}ber many-one lokal-selbstreduzierbare Mengen
09.55-10.20 Uhr A. Kick, Karlsruhe:
Erzeugung von Gegenbeispielen beim globalen µ-Kalk{\"u}l Model checking
10.20-10.45 Uhr M. Kutyowski, K. Lorys, T. Wierzbicki, Paderborn, Wroclaw:
Complexity of Boolean functions on QRQW and EREW PRAMs

10.45-11.15 Uhr Pause

11.15-11.40 Uhr J. Rethmann, E. Wanke, D{\"u}sseldorf:
Storage Controlled Pile-Up Systems
11.40-12.05Uhr K. Jansen, J. Reiter, M{\"u}nchen, Trier:
Approximation Algorithms for Register Allocation
12.05-12.30 Uhr M. B{\"o}hm, P. Heusch, F. Meisgen, T. Seifert, E. Speckenmeyer, K{\"o}ln:
Precomputation-based Load Balancing

12.30-14.00 Uhr Mittagspause

14.00-14.25 Uhr K. K{\"u}hnle, E. W. Mayr, M{\"u}nchen:
Exponential space computation of G bases
14.25-14.50 Uhr U. Koppenhagen, E. W. Mayr, M{\"u}nchen:
The Complexity of the Equivalence Problem for Commutative Semigroups
14.50-15.15 Uhr O. Kullmann, Frankfurt:
Worst case-Analyse und untere Schranken f{\"u}r bessere SAT-Algorithmen

15.15-15.45 Uhr Pause

15.45-16.10 Uhr A. Hett, R. Drechsler, B. Becker, Freiburg:
MORE: Alternative Implementation of BDD-Packages by Multi-Operand Synthesis
16.10-16.35 Uhr Ch. Meinel, A. Slobodov, Trier:
Ein neuer Reduktionsbegriff f{\"u}r OBDDs
16.35-17.00 Uhr T. Theobald, Ch. Meinel, Trier:
Zustandscodierungen und OBDD-Gr{\"o}{\"s}en", } @InCollection{zpr96-220, author = "A. Bachem and A. Hamacher and C. Moll and G. Raspel", institution = mi, title = "Optimale Linienf{\"u}hrung und Routenplanung in Verkehrssystemen", booktitle = "Mathematik: Schl{\"u}{\"s}eltechnologie fuer die Zukunft. Verbundprojekte zwischen Universit{\"a}t und Industrie", editor = "K.-H. Hoffmann et al.", location = "Berlin, Germany", publisher = "Springer-Verlag", pages = "626--636", year = "1997", crindex = "219k,11,zpr96-220.ps.gz", keywords = "vehicle routing, heuristics, time windows, minimal spanning tree, matching, shortest path, traffic simulation; 90B06, 90C27, 05C05, 05C90, 05C70, 05C38", annote = "This paper decribes vehicle routing problems appearing at a specific company, the Gerresheimer Glas AG. There are two different kind of problems: a full load routing problem and a multi-depot partial load delivery problem. We introduce algorithms that solve these problems and discuss modifications and alternatives for our specific practical constraints. Another approach to minimize the overall distance covered by empty trucks is the idea of introducing reload stations. This leads to the mathematical formulation of Steiner problems. For all these problems a good calculation of the driving times is necessary to employ the algorithms on practical problems. In this context a short overview over traffic simulation systems is given. At last the software engineering problems of dispositions systems are discussed.", } @InProceedings{zpr96-219, author = "M. B{\"o}hm and E. Speckenmeyer", institution = inf, title = "Precomputation-based Load Balancing", booktitle = "Proceedings of the 4th Workshop on Parallel Systems \& Algorithms PASA '96", editor = "F. Ho{\"s}feld and E. Maehle and E. W. Mayer", publisher = "World Scientific", pages = "177--194", year = "1997", crindex = "67k,15,zpr96-219.ps.gz", keywords = "load balancing, distributed computing, satisfiability problem; 68Q22, 68Q25, 68T20", annote = "An algorithm, called PLB is introduced, which redistributes workload in a processor network N in order to supply every processor of N with (about) the same amount of workload. PLB is defined in its basic form for trees, but can be extended to other topologies. The redistribution is done locally on the basis of information of over- or underload in subnetworks of N. We show, that PLB performs O(d) steps, only, where d denotes the diameter of N, and in the average case at most four times as many workload has to be migrated in complete binary trees compared to clique networks, the best possible networks. We describe an implementation of PLB and present experimental results when solving the Boolean satisfiability problem, demonstrating that PLB performs very well in practice.", } @InProceedings{zpr96-218, author = "T. Seifert and E. Speckenmeyer", institution = inf, title = "Optimal Oblivious Permutation Routing in Small Hypercubes", booktitle = "Parallel-Algorithmen, -Rechnerstrukturen und -Systemsoftware, Proc. 4. PASA Workshop 1996, J{\"u}lich", year = "1996", pages = "53--66", crindex = "63k,11,zpr96-218.ps.gz", keywords = "Routing, Oblivious Routing, Hypercubes, Permutations; 94C99", annote = "For each $d\le 8$ we provide an oblivious algorithm for routing any permutation on the d-dimensional hypercube in at most d communication steps. To prove our result we show that any 1-to-2d'-routing problem and any 2d'-to-1-routing problem can be solved in at most d' $(d'\le 4)$ coummunication steps on a d'-dimensional hypercube. Furthermore we present a class of efficiently working routing algorithms which allows us to make an improved statement about the complexity of some of the provided algorithms.", } @Article{zpr96-217, author = "C. De Simone and M. Diehl and M. J{\"u}nger and P. Mutzel and G. Reinelt and G. Rinaldi", institution = inf, title = "Exact Ground States of Two-Dimensional +-{J} Ising Spin Glasses", journal = "Journal of Statistical Physics", volume = "84", number = "5/6", pages = "1363--1371", year = "1996", crindex = "139k,12,zpr96-217.ps.gz", keywords = "branch-and-cut, spin glasses, ground states; 82D30, 90C", annote = "In this paper we study the problem of finding an exact ground state of a two-dimensional ±J Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is a concentration p of negative bonds, with p ranging between 0.1 and 0.9. With our exact algorithm we can determine ground states of grids of sizes up to 50×50 in a moderate amount of computation time (up to one hour each) for several values of p. For the ground state energy of an infinite spin glass system with p=0.5 we estimate E0.5\infty = -1.4015 ±0.0008.
We report on extensive computational tests based on more than 22,000 experiments.", } @TechReport{zpr96-216, author = "M. Wottawa", institution = mi, title = "{PACKLIB}: Ein {ASCII}-Datenformat f{\"u}r Packungsprobleme", year = "1996", crindex = "49k,15,zpr96-216.ps.gz", keywords = "Packungsproblem, Klassifizierung, Problemdatenbank; 90B05,90-08", annote = "{\"A}hnlich der TSPLIB von G. Reinelt f{\"u}r Traveling-Salesman-Probleme definieren wir ein Datenformat f{\"u}r Packungsprobleme und stellen mit diesem eine Sammlung von Problemen aus der Literatur vor. Das Format benutzt ausschlie{\ss}lich ASCII-Zeichen und ist somit auf beliebige Computersysteme {\"u}bertragbar. Die aus der Literatur bekannten Probleminstanzen sind in diesem neuen PACKLIB-Format unter der FTP-Adresse ftp://ftp.zpr.uni-koeln.de/pub/packlib bereitgestellt. Eine HTML-Version dieses Dokumentes ist unter http://www.zpr.uni-koeln.de/~paralor/packlib/packlib.html zu finden.", } @TechReport{zpr96-215, author = "M. J{\"u}nger and V. Kaibel", institution = inf, title = "A Basic Study of the {QAP}-Polytope", year = "1996", crindex = "102k,20,zpr96-215.ps.gz", keywords = "Quadratic Assignment Problem, Polyhedral Combinatorics, QAP-Polytope; 90C09, 90C10, 90C27", annote = "We investigate a polytope (the `QAP-Polytope') beyond a `natural' integer programming formulation of the Quadratic Assignment Problem (QAP) that has been used successfully in order to compute good lower bounds for the QAP in the very recent years. We present basic structural properties of the QAP-Polytope, partially independently also obtained by Rijal (1995). The main original contribution of this work is the representation of the QAP-Polytope in a space different from the one in which it is defined naturally. This representation provides us with a much simpler way to derive the dimension of the QAP-Polytope, as well as to investigate the facial structure of it. Furthermore, it leads to some interesting observations concerning the combinatorial structure of the QAP-Polytope.", } @InProceedings{zpr95-214, author = "P. Wagner", booktitle = "Traffic and Granular Flow 1995", institution = mi, note = "Conference Proceedings", title = "Traffic simulations using cellular automata: comparison with reality", year = "1995", crindex = "130k,5,zpr95-214.ps.gz", keywords = "traffic simulation, cellular automata, lane changing; 65C20, 90B20, 60J20, 82C22, 82B41", annote = "In this article we summarize work concerned with the comparison between a cellular automaton (CA)-model for traffic flow and empirical data. The results presented here consist of two parts: comparing the fundamental diagrams and looking for a certain set of lane changing rules, which reproduce at least qualitatively the data measured on german motorways. These last results indicate, that it is possible to design microscopic lane changing rules that give the correct macroscopic behaviour regarding the lane-usage versus flow curves. To obtain such curves has been the problem in recent investigations using another microscopic model.", } @Article{zpr95-213, author = "M. Rickert and K. Nagel and M. Schreckenberg and A. Latour", institution = mi, title = "Two Lane Traffic Simulations using Cellular Automats", journal = "Physica A", volume = "231", number = "4", pages = "534--550", year = "1996", crindex = "1055k,17,zpr95-213.ps.gz", keywords = "traffic simulation, cellular automata, lane changing; 65C20, 90B20, 60J20, 82C22, 82B41", annote = "We examine a simple two lane cellular automaton based upon the single lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.", } @Article{zpr95-212a, author = "A. Srivastav and P. Stangier", institution = inf, title = "Tight Approximation for Resource Constrained Scheduling and Bin Packing", journal = "Discrete Applied Mathematics", note = "Proc. of the 4th Twente Workshop on Graphs and Combinatorial Optimization (Enschede, 1995)", volume = "79", number = "1-3", year = "1997", pages = "223--245", keywords = "resource constrained scheduling, multidimensional bin packing, randomized algorithm, derandomization, approximation algorithm, chromatic index; 60C05, 60E15, 68Q25, 90C10, 90B35", annote = "We consider the following resource constrained scheduling problem. Given m identical processors, s resources with upper bounds, n independent tasks of unit length, where each task has a start time and requires one processor and a task-dependent amount of every resource.
The optimization problem is to schedule all tasks at discrete times in N, minimizing the latest completion time Cmax subject to the processor, resource and start-time constraints. Multidimensional bin packing is a special case of this problem. The problem is NP-hard even under much simpler assumptions. In case of zero start times R{\"o}ck and Schmidt (1983) showed an (m/2)-factor approximation algorithm and de la Vega and Lueker (1981), improving a classical result of Garey, Graham, Johnson and Yao (1976), gave for every $\epsilon > 0$ a linear time algorithm with an asymptotic approximation guarantee of $s +\epsilon$.
The contribution of this paper is to break the O(m) resp. O(s) barrier, even in the case of zero start times, at least for problems where the number of processors and the resource bounds are in $\Omega(\log |I|)$, |I| being the input size of the problem. The main results are constant factor approximation algorithms for such problems and the proof of the optimality of the achieved approximation under the hypothesis $P \not= NP$.", } @InProceedings{zpr95-212, author = "A. Srivastav and P. Stangier", institution = inf, title = "Tight Approximation for Resource Constrained Scheduling and Bin Packing", booktitle = "Proceedings of the Second Annual European Symposium on Algorithms (ESA '94)", editor = "J. van Leeuwen", pages = "307--318", publisher = "Springer-Verlag", series = "Lecture Notes in Computer Science", volume = "855", year = "1994", crindex = "95k,24,zpr95-212.ps.gz", keywords = "resource constrained scheduling, multidimensional bin packing, randomized algorithm, derandomization, approximation algorithm, chromatic index; 60C05, 60E15, 68Q25, 90C10, 90B35", annote = "We consider the following resource constrained scheduling problem. Given m identical processors, s resources with upper bounds, n independent tasks of unit length, where each task has a start time and requires one processor and a task-dependent amount of every resource.
The optimization problem is to schedule all tasks at discrete times in N, minimizing the latest completion time Cmax subject to the processor, resource and start-time constraints. Multidimensional bin packing is a special case of this problem. The problem is NP-hard even under much simpler assumptions. In case of zero start times R{\"o}ck and Schmidt (1983) showed an (m/2)-factor approximation algorithm and de la Vega and Lueker (1981), improving a classical result of Garey, Graham, Johnson and Yao (1976), gave for every $\epsilon > 0$ a linear time algorithm with an asymptotic approximation guarantee of $s +\epsilon$.
The contribution of this paper is to break the O(m) resp. O(s) barrier, even in the case of zero start times, at least for problems where the number of processors and the resource bounds are in $\Omega(\log |I|)$, |I| being the input size of the problem. The main results are constant factor approximation algorithms for such problems and the proof of the optimality of the achieved approximation under the hypothesis $P \not= NP$.", } @PhdThesis{zpr95-211, author = "S. Kromberg", school = mi, title = "Adjoints, Schiefk{\"o}rper und algebraische Matroide", year = "1995", crindex = "424k,153,zpr95-211.ps.gz", keywords = "matroids, oriented matroids, duality, adjoint, linear representation, algebraic representation, skew fields, configuration of pseudopoints; 05B35, 06C10, 12E15, 52B40", annote = "Im Mittelpunkt des ersten Teils der Arbeit steht der zweite Dualit{\"a}tsbegriff der Matroidtheorie, der Begriff des Adjoints eines geometrischen Verbandes. Es ist bekannt, da{\ss} iterierte Adjointbildung gegen eine projektive Geometrie konvergiert, so da{\ss} die Untersuchung von Adjoints Einsicht in geometrische Gr{\"u}nde f{\"u}r die Nichtlinearit{\"a}t von Matroiden gibt. Wir zeigen, da{\ss} Copunkterweiterungen durch Coparallele f{\"u}r (orientierte) Matroide vom Rang 3 stets auf (orientierte) Matroide mit Adjoint f{\"u}hren und geben erstmalig ein orientierbares Matroid an, das einen orientierten Adjoint besitzt, soda\ss jedoch jeder Adjoint dieses Matroids selbst keinen Adjoint besitzt.
Ein weiterer Schwerpunkt der Arbeit sind lineare Darstellungen von (orientierten) Matroiden {\"u}ber (geordneten) Schiefk{\"o}rpern. Unsere Wiederentdeckung von (geordneten) Schiefk{\"o}rper erm{\"o}glicht uns die Konstruktion eines (orientierten) Adjoints zum Dual des Non-Pappus-Matroids und die Beantwortung einer Frage von J. Richter-Gebert, der nach der Existenz eines Adjoints zu einem bestimmten orientierten Matroid gefragt hatte. Wir zeigen, da{\ss} jenes Matroid linear {\"u}ber einem geordneten Schiefk{\"o}rper ist und daher einen Adjoint besitzt.
Im letzten Teil der Arbeit behandeln wir algebraische Darstellungen von Matroiden. Der systematische Aufbau der Theorie gestattet uns, neue - meist k{\"u}rzere - Beweise f{\"u}r einige bekannte Resultate zu algebraischen Matroiden zu geben. Wir zeigen, da{\ss} die st{\"a}rkste bekannte kombinatorische Eigenschaft algebraischer Matroide nicht hinreichend daf{\"u}r ist, da{\ss} ein Matroid algebraisch ist, und diskutieren einen aussichtsreichen Kandidaten f{\"u}r die (negative) Entscheidung der Frage nach der Algebraizit{\"a}t des Duals eines algebraischen Matroids. Zum Abschlu{\ss} geben wir ein auf Gr{\"o}bner-Basen beruhendes algorithmisches Verfahren an, das zu einer gegebenen algebraischen Darstellung eines Matroids das dargestellte Matroid bestimmt.", } @TechReport{zpr95-210, author = "M. Neschen and F. N{\"u}bel", title = "{COGNITUS} - Fast and Reliable Recognition of Handwritten Forms based on Vector Quantisation", year = "1996", crindex = "46k,6,zpr95-210.ps.gz", keywords = "Character recognition, pattern recognition, embedded systems, high-performance computing; 68T10", annote = "We report on an efficient intelligent character recognition tool for the automatic treatment of handwritten bank transfer forms. The classification is based on nearest-neighbor algorithms and a novel binary clustering technique for the generation of large prototype sets. We introduce a new confidence measure which can be used on a decision tree structure to combine lowest error rates with a very high recognition speed. Likelihood vectors allow context correction by database queries based on dynamic programming techniques as well as an easy integration of different classifier approaches in a multi-agent environment. In this paper, we present all components of the prototype system and give details on its realization and on possible parallel implementations on embedded systems.", } @TechReport{zpr95-209, author = "W. Hochst{\"a}ttler and J. Nesetril", institution = mi, title = "Linear Programming Duality and Morphisms", year = "1995", crindex = "63k,23,zpr95-209.ps.gz", keywords = "oriented matroids, strong map, homomorphism, duality; 05B35, 05C99, 18B99, 90C05", annote = "In this paper we investigate the class $NP \cap co$-$NP$ (or the class of problems permitting a good characterisation) from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids.", } @Article{zpr95-208a, author = "S. P. Fekete and S. Khuller and M. Klemmstein and B. Raghavachari and N. Young", institution = mi, title = "A network-flow technique for finding low-weight bounded-degree spanning trees", journal = "Journal of Algorithms", year = "1997", volume = "24", number = "2", month = aug, pages = "310--324", crindex = "73k,12,zpr95-208.ps.gz", keywords = "mathematical programming, graph theory, graph algorithms, approximation, network-flows bounded degree; 05C05, 05C12, 05C85, 90B10, 90C27, 90C35", annote = "Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, we consider the problem of computing a low weight spanning tree such that the degree of each vertex is at most its specified bound. In particular, we give efficient algorithms for modifying a given spanning tree T to meet the degree constraints. These algorithms are optimal in the following sense: We show that in the worst case, the weight of the tree increases by at most a factor of $2 - \min\Big\{\frac{\goal(v)-2}{\degree_T(v)-2} : \degree_{T}(v)>2\Big\},$ where $\goal(v) \ge 2$ is the desired degree of vertex $v$ and $\degree_T(v)$ is the initial degree; we also show that this factor is best possible. We conclude the paper by discussing geometric aspects of the problem.", } @InProceedings{zpr95-208, author = "S. P. Fekete and S. Khuller and M. Klemmstein and B. Raghavachari and N. Young", institution = mi, title = "A network-flow technique for finding low-weight bounded-degree trees", booktitle = "Proceedings of the 5th International Integer Programming and Combinatorial Optimization IPCO Conference. 3-5 Jun 1996. Vancouver, British Columbia, Canada", editor = "W. H. Cunningham and S. T. McCormick and M. Queyranne", series = "Lecture Notes in Computer Science", publisher = "Springer-Verlag", volume = "1084", year = "1996", pages = "105--117", crindex = "73k,12, zpr95-208.ps.gz", keywords = "mathematical programming, graph theory, graph algorithms, approximation, network-flows bounded degree; 05C05, 05C12, 05C85, 90B10, 90C27, 90C35", annote = "Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, we consider the problem of computing a low weight spanning tree such that the degree of each vertex is at most its specified bound. In particular, we give efficient algorithms for modifying a given spanning tree T to meet the degree constraints. These algorithms are optimal in the following sense: We show that in the worst case, the weight of the tree increases by at most a factor of $2 - \min\Big\{\frac{\goal(v)-2}{\degree_T(v)-2} : \degree_{T}(v)>2\Big\},$ where $\goal(v) \ge 2$ is the desired degree of vertex $v$ and $\degree_T(v)$ is the initial degree; we also show that this factor is best possible. We conclude the paper by discussing geometric aspects of the problem.", } @InProceedings{zpr95-207, author = "S. P. Fekete and M. Houle and S. Whitesides", institution = mi, title = "New results on a visibility representation of graphs in 3{D}", booktitle = "Proc. of the Symposiumon Graph Drawing '95", location = "Passau, Germany", editor = "F. J. Brandenburg", year = "1996", pages = "234--241", series = "Lecture Notes in Computer Science", volume = "1027", publisher = "Springer-Verlag", crindex = "54k,9,zpr95-207.ps.gz", keywords = "graph representation, visibility, graph drawing, 3-dimensional geometry; 05C10, 05C75, 68R05, 68R10", annote = "This paper considers a 3-dimensional visibility representation of cliques Kn. In this representation, the objects representing the vertices are 2-dimensional and lie parallel to the x,y-plane, and two vertices of the graph are adjacent if and only if their corresponding objects see each other by a line of sight parallel to the z-axis that intersects the interiors of the objects. In particular, we represent vertices by unit discs and by discs of arbitrary radii (possibly different for different vertices); we also represent vertices by axis-aligned unit squares, by axis-aligned squares of arbitrary size (possibly different for different vertices), and by axis-aligned rectangles. We present:

", } @InProceedings{zpr95-206, author = "S. P. Fekete", institution = mi, title = "Finding all anchored squares in a convex polygon in subquadratic time", booktitle = "Proceedings of the Fourth Canadian Conference on Computational Geometry", pages = "71--76", year = "1992", location = "St. John's, Newfoundland, Canada", month = aug, crindex = "39k,6,zpr95-206.ps.gz", keywords = "theoretical computer science, computational geometry, polygons, convex sets, inscribed squares, pattern recognition; 52A10, 52B55, 68Q20, 68U05", annote = "We present an O(n log2(n)) method that finds all squares inscribed in a convex polygon with n vertices such that at least one corner lies on a vertex of the polygon.

This is a revised version of the published paper.", } @TechReport{zpr95-205a, author = "P. Bose and H. Everett and S. P. Fekete and A. Lubiw and H. Meijer and K. Romanik and T. Shermer and S. Whitesides", institution = mi, title = "On a visibility representation for graphs in three dimensions", booktitle = "Snapshots of Computational and Discrete Geometry", volume = "3", pages = "2--25", editor = "D. Avis and P. Bose", year = "1994", crindex = "97k,15,zpr95-205.ps.gz", keywords = "graph representation, visibility, graph drawing, 3-dimensional geometry; 05C10, 05C75,68R05, 68R10", } @InProceedings{zpr95-205, author = "P. Bose and H. Everett and S. P. Fekete and A. Lubiw and H. Meijer and K. Romanik and T. Shermer and S. Whitesides", institution = mi, booktitle = "Proc. Graph Drawing '93, ALCOM International Workshop PARIS 1993 on Graph Drawing and Topological Graph Algorithms", title = "On a visibility representation for graphs in three dimensions", year = "1993", pages = "38--39", location = "S\`evres, France", month = sep, crindex = "97k,15,zpr95-205.ps.gz", keywords = "graph representation, visibility, graph drawing, 3-dimensional geometry; 05C10, 05C75,68R05, 68R10", annote = "Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. Application areas such as VLSI wire routing and circuit board layout have stimulated research on visibility representations where the sets belong to R2. Here, motivated by the emerging research area of graph drawing, we study a 3-dimensional visibility representation.
In this representation, each vertex of the graph maps to a closed rectangle in R3 such that the rectangles are disjoint, the planes determined by the rectangles are perpendicular to the z-axis, and the sides of the rectangles are parallel to the x- or y-axes. Edges are expressed by the following visibility relation. Two rectangles Ri and Rj are considered visible provided that there exists a closed cylinder C of non-zero radius such that the ends of C are contained in Ri and Rj, the axis of C is parallel to the z-axis, and C does not intersect any other rectangle.
Our main results are as follows. All planar graphs have a representation, as do many non-planar graphs. In particular, a complete graph Kn has a representation for values of n<=20. However, a complete graph Kn does not have a representation for n>=103. (Recently, this bound has been improved to 56 by Fekete, Houle, and Whitesides, using extensions of the techniques presented here.) The complete bipartite graph Km,n has a representation for all m and n. Finally, we show that the family of graphs with a representation is not closed under graph minors.

This is an extended version of the published paper.", } @InProceedings{zpr95-204, author = "S. P. Fekete and M. Klemmstein", institution = mi, title = "Worst-case ratios for bounded-degree trees", booktitle = "Proceedings of the 4th Biannual Twente Workshop on Graph Theory and Discrete Optimization", year = "1995", pages = "103--106", crindex = "48k,6,zpr95-204.ps.gz", keywords = "mathematical programming, graph theory, graph algorithms, approximation, spanning tree, bounded degree; 05C05, 05C12, 05C85, 90B10, 90C27, 90C35", annote = "We discuss problems of minimum degree-constrained trees Tk, where each vertex of a complete graph Kn with a metric satifying triangle inequality is restricted to at most k neighbors. We show that for any k and m, the ratio w(Tk)/w(Tk+m) can be arbitrarily close to rhok,m=1 + m/(m+k-2) and give an O(nlog (k+m)) algorithm that converts a Tk+m into a Tk such that w(Tk)< rhok,m Tk+m. For the special case of a planar point set with $L1$ distances, this implies that we can find a T3 with w(T3)/w(Tmin) <= 3/2.", } @InProceedings{zpr95-203, author = "M. J{\"u}nger and P. Mutzel", institution = inf, title = "Exact and Heuristic Algorithms for 2-Layer Straightline Crossing Minimization", booktitle = "Proc. Symposium on Graph Drawing '95", location = "Passau, Germany", editor = "F. Brandenburg", publisher = "Springer-Verlag", series = "Lecture Notes in Computer Science", number = "1027", year = "1996", crindex = "85k,13,zpr95-203.ps.gz", keywords = "automatic graph drawing, crossing minimization, linear ordering, polyhedral combinatorics, branch-and-cut, crossing number, 2-layered networks, feedback arcset, graph drawing; 68R10, 90C27, 90C10, 05C10", annote = "We present algorithms for the 2-layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NP-hard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes. For bigger instances, the iterated barycenter method turns out to be the method of choice among several popular heuristics whose performance we could assess by comparing the results to optimum solutions.", } @TechReport{zpr95-202, author = "W. Hochst{\"a}ttler and M. Loebl", institution = mi, title = "On Bases of Circuit Lattices", year = "1995", crindex = "58k,15,zpr95-202.ps.gz", keywords = "geometry of numbers, binary matroids, lattice basis; 05B40, 11H31, 52C17", annote = "Our aim is to propose and study the following conjecture. There exists a set of cycles of each binary matroid B, which form a basis of the integer lattice generated by the circuits of B.", } @Article{zpr95-201, author = "M. J{\"u}nger and P. Mutzel and T. Odenthal and M. Scharbrodt", institution = inf, title = "The thickness of a minor-excluded class of graphs", note = "Graph theory (Lake Bled, 1995)", journal = "Discrete Mathematics", volume = "182", number = "1-3", pages = "169--176", month = mar, year = "1998", crindex = "70k,8,zpr95-201.ps.gz", keywords = "thickness, crossing number, skewness, graph-minor, 1-sum, 2-sum, delta-sum, topological graph theory, k5-free graphs, decomposition theorem, planar subgraph; 05C10, 05C70, 05C85, 68R10, 90C27", annote = "The thickness problem on graphs is NP-hard and only few results concerning this graph invariant are known. Using a decomposition theorem of Truemper, we show that the thickness of the class of graphs without G12-minors is less than or equal to two (and therefore, the same is true for the more well-known class of the graphs without K5-minors). Consequently, the thickness of this class of graphs can be determined with a planarity testing algorithm in linear time.", } @TechReport{zpr95-200, author = "W. Hochst{\"a}ttler", institution = mi, title = "Oriented Matroids from Wild Spheres", year = "1995", crindex = "66k,14,zpr95-200.ps.gz", keywords = "oriented matroids, wild sphere, sphere system, topology, matroids, geometry; 05B35, 06B30, 51D20, 52B30, 52B40, 57N50", annote = "In a recent article [5] we gave a lattice-theoretical characterization of oriented matroids in terms of the zero-map. In this paper we derive from that characterization a generalization of one direction of the Topological Representation Theorem using hyperspheres which may be wildly embedded, thus solving a problem presented by A. Bj{\"o}rner et al. [Oriented Matroids (1993), Exercise 5.6.c].", } @InProceedings{zpr95-199, author = "A. Hamacher and C. Moll", institution = mi, title = "The Euclidian Traveling Salesman Selection Problem", booktitle = "OR Proceedings of SOR '95", year = "1995", crindex = "45k,7,zpr95-199.ps.gz", keywords = "traveling salesman problem, branch-and-bound, Dynamic Programming", annote = "The traveling salesman problem (TSP) is one of the famous problems of combinatorial optimization. In this paper a generalization of the TSP, the traveling salesman selection problem (TSSP) is introduced. The problem is restricted to the Euclidian case where the TSP can be formulated as follows: Given n cities in the plane and their Euclidian distances, the problem is to find the shortest TSP-tour, i.e. a closed path visiting each of the n cities exactly once.
In addition to that the TSSP specifies a number k The main purpose of this paper is the presentation of an exact algorithm for the TSSP. It is based on a geometrical procedure searching for all clusters of about k nodes which can contain the shortest k-tour. These clusters are the start set for a branch-and-bound procedure that determines the shortest k-tour in each cluster and therefore the exact solution of the TSSP. A dynamic programming approach for calculating shortest t-chains is used to obtain a lower bound for the branch-and-bound algorithm.", } @InProceedings{zpr95-198, author = "J. Schepers and M. Wottawa", institution = mi, title = "Warehouse Optimization: Packing-algorithms for goods with complex geometries", booktitle = "Operations Research Proceedings 1995", editor = "P. Kleinschmidt and A. Bachem and U. Derigs and D. Fischer and U. Leopold-Wildburger and R. M{\"o}hring", publisher = "Springer-Verlag", pages = "125--131", year = "1996", crindex = "36k,6,zpr95-198.ps.gz", keywords = "packing, complex geometry, heuristics; 90B06, 90-08, 68R99, 90C27", annote = "In the organization of a warehouse one has to optimize different work routines such as shortest-path-problems, three-dimensional packing problems and assignment/placement problems. Within the framework of the implementation of an integrated warehouse optimization system we started to deal with the packing problems and their integration into algorithms for vehicle routing problems. In this talk we present a practical packing problem arising from the packing of bathtubs and other goods with complex geometry on pallets. We model this problem both as a packing problem and as a vehicle routing problem and discuss suitable algorithms and present some computational results.", } @Article{zpr95-197, author = "B. Albers and A. Bachem and R. Heesen and W. Hochst{\"a}ttler", institution = mi, title = "Benchmarking und Leistungsvergleich in Filialnetzen gro{\ss}er Unternehmen", journal = "Zeitschrift f{\"u}r Betriebswirtschaft", volume = "66", pages = "1313--1328", year = "1996", crindex = "75k,19, zpr95-197.ps.gz", keywords = "manpower planning; 90B70", annote = "Rationalisierung und Benchmarking sind in der heutigen Zeit Schlagw{\"o}rter zur Effizienzsteigerung im Unternehmen. Gerade Unternehmen mit gro{\ss}em Filialnetz sind aufgefordert, Rationalisierungs- und Flexibilisierungspotentiale aufzudecken und umzusetzen, um wettbewerbsf{\"a}hig bleiben zu k{\"o}nnen. In diesem Aufsatz haben wir einen Ansatz zur Quantifizierung der Arbeitsproduktivit{\"a}t im Dienstleistungsbereich im Hinblick auf Benchmarking und Leistungsvergleiche f{\"u}r Unternehmen mit gro{\ss}en Filialnetzen vorgestellt. Er beruht auf neuen mathematischen Konzepten, die anhand praktischer Daten aus dem Dienstleistungsbereich bereits erfolgreich angewendet wurden.", } @TechReport{zpr95-196, author = "A. Bachem and R. Heesen", institution = mi, title = "Ein sicheres Zahlungssystem f{\"u}r offene Computernetze", year = "1995", crindex = "60k,10,zpr95-196.ps.gz", keywords = "electronic cash, digital cash, electronic commerce; 94A99", annote = "Durch den fortschreitenden Anschlu{\ss} von Computern an ein weltweites Netzwerk entstehen neue M{\"a}rkte, auf denen Waren erworben, Informationen genutzt oder Dienstleistungen in Anspruch genommen werden k{\"o}nnen. Handel und Banken sind aufgefordert, sich rechtzeitig zu positionieren, um nicht zuk{\"u}nftig Marktanteile zu verlieren.", } @Article{zpr95-195, author = "W. Hochst{\"a}ttler and S. Kromberg", institution = mi, title = "A Pseudoconfiguration of Points without Adjoint", journal = "Journal of Combinatorial Theory B", pages = "277--294", volume = "68", number = "2", year = "1996", crindex = "76k,17,pr95-195.ps.gz", keywords = "matroids, oriented matroids, adjoints, duality, configuration of pseudopoints; 05B35, 06C10, 52B40", annote = "We give an example of a simple oriented matroid $\cal D$ that admits an oriented adjoint. Already any adjoint of the underlying matroid D, however, does itself not admit an adjoint. D arises from the wellknown Non-Desargues-Matroid by a coextension by a coparallel element and, hence, has rank 4. The orientability of D and some of its adjoints follows from an apparantly new oriented matroid construction given in the paper that is a very special case of an amalgam of two copies of one oriented matroid.", } @Article{zpr95-194, author = "A. Bachem and R. Heesen and J.-T. Pfenning", institution = mi, title = "Digitales Geld f{\"u}r das Internet", journal = "Zeitschrift f{\"u}r Betriebswirtschaft", volume = "66", number = "6", year = "1996", pages = "697--714", crindex = "152k,22,zpr95-194.ps.gz", keywords = "electronic cash, digital cash, electronic commerce; 94A99", annote = "Durch den fortschreitenden Anschlu{\ss} von Computern an ein weltweites Netzwerk entstehen neue M{\"a}rkte, auf denen Netzwerkressourcen und Informationsangebote in Netzen gegen Entgelt genutzt, Waren erworben oder Dienstleistungen in Anspruch genommen werden k{\"o}nnen. Speziell f{\"u}r diesen Zweck wurden Konzepte f{\"u}r elektronisches Geld entwickelt, die eine vergleichbare Flexibilit{\"a}t, F{\"a}lschungssicherheit und Anonymit{\"a}t wie Bargeld aufweisen. In diesem Artikel haben wir einen {\"U}berblick {\"u}ber Online-Anbieter gegeben und Sicherheitskonzepte sowie elektronische Zahlungsmittel f{\"u}r das Internet kurz vorgestellt.", } @Article{zpr95-193, author = "J.-T. Pfenning and R. Minnich and A. Bachem", institution = mi, title = "Virtual Shared Memory Programming on Workstation Clusters", journal = "Future Generation Computer Systems", publisher = "Elsevier Science B. V.", pages = "387--399", volume = "11", number = "4/5", month = aug, year = "1995", crindex = "157k,15,zpr95-193.ps.gz", annote = "Workstation clusters have recently attracted high interest as a technology providing supercomputer class performance at much lower price levels. Today the message passing programming model dominates the application development, despite the overhead and the complexity introduced by the explicitly coded data transfers. We give an introduction to the virtual shared memory programming model and report on the experiences with the MNFS system. We show that shared memory with weak coherency can perform competitive to message passing and provide an excellent tool for parallelizing programs using complex data structures with dynamic load balancing.", } @PhdThesis{zpr95-192, author = "C. Moll", school = mi, title = "Das inverse {K}{\"u}rzeste-Wege-Problem", pages = "83", year = "1995", crindex = "199k,85,zpr95-192.ps.gz", keywords = "graph theoretic problems, shortest path problem, inverse shortest path problem, weight function, shortest path distances, NP-completeness, disjoint paths problem, linear programming duality, minimum cost multicommodity flow problem, NP-hard; 05C85, 90C35, 05C38, 68R10, 90B10", annote = "In der Arbeit wird die Frage untersucht, was man f{\"u}r Aussagen {\"u}ber die Gewichte eines Graphen machen kann, wenn man die Kanten des Graphen und Distanzen zwischen einzelnen Knoten kennt.
Die Arbeit umfa{\ss}t einige Vollst{\"a}ndigkeitsaussagen. Au{\ss}erdem wird der Zusammenhang zwischen Mehrg{\"u}terflu{\ss}problemen und dem inversen K{\"u}rzeste-Wege-Problem aufgearbeitet.
Desweiteren umfa{\ss}t die Arbeit zusammenfassende Kapitel zur Komplexit{\"a}tstheorie und zur Linearen Programmierung, die der Autor gerade auch f{\"u}r Nicht-Profis geschrieben hat.", } @TechReport{zpr95-191, author = "M. J{\"u}nger and P. St{\"o}rmer", institution = inf, title = "Solving large-scale traveling salesman problems with parallel Branch-and-Cut", year = "1995", crindex = "96k,35,zpr95-191.ps.gz", keywords = "branch-and-cut, parallel, traveling salesman problem, symmetric traveling salesman problem; 90C27", annote = "We introduce the implementation of a parallel Branch-and-Cut algorithm to solve large-scale traveling salesman problems.
Rather than using the well-known models of homogeneous distribution and simple Master/Slave communication, we present a more sophisticated distribution that takes the advantage of several independent features of a Branch-and-Cut code. Computational results are reported for several instances of the TSPLIB.", } @TechReport{zpr95-190, author = "G. Wambach and H. Wettig", institution = inf, title = "Block Sieving Algorithms", year = "1995", crindex = "42k,9,zpr95-190.ps.gz", keywords = "MPQS, RISC, Program Optimization, Memory Design, Factorization; 11Y05, 68-04", annote = "Quite similiar to the Sieve of Erastosthenes, the best-known general algorithms for factoring large numbers today are memory-bounded processes. We develop three variations of the sieving phase and discuss them in detail. The fastest modification is tailored to RISC processors and therefore especially suited for modern workstations and massively parallel supercomputers. For a 116 decimal digit composite number we achieved a speedup greater than two on an IBM RS/6000 250 workstation.", } @Article{zpr95-189a, author = "P. Heusch", institution = inf, title = "The Complexity of the Falsifiability Problem for Pure Implicational Formulas", journal = "Discrete Applied Mathematics", volume = "96-97", number = "1-3", year = "1999", pages = "127--138", keywords = "algorithms, data structure, logic in computer science, NP-complete; 68T15, 68Q15, 03B99", annote = "We consider Boolean formulas where logical implication (->) is the only operator and all variables, except at most one (denoted z), occur at most twice. We show that the problem of determining falsifiability for formulas of this class is NP-complete but if the number of occurrences of z is restricted to be at most k then there is an O(|F|) algorithm for certifying falsifiability. We show this hierarchy of formulas, indexed on k, is interesting because even lower levels (e.g., k=2) are not subsumed by several well-known polynomial time solvable classes of formulas.", } @InProceedings{zpr95-189, author = "P. Heusch", institution = inf, title = "The Complexity of the Falsifiability Problem for Pure Implicational Formulas", booktitle = "Proceedings of the 20th International Symposium, Mathematical Foundations of Computer Science. MFCS '95. 28 Aug - 1 Sep 1995. Prague, Czech Republic", editor = "J. Wiedermann and P. Hajek", publisher = "Springer-Verlag", series = "Lecture Notes in Computer Science", volume = "969", pages = "221--226", year = "1995", crindex = "44k,8,zpr95-189.ps.gz", keywords = "algorithms, data structure, logic in computer science, NP-complete; 68T15, 68Q15, 03B99", annote = "Since it is unlikely that any NP-complete problem will ever be efficiently solvable, one is interested in identifying those special cases that can be solved in polynomial time. We deal with the special case of Boolean formulas where the logical implication $\ra$ is the only operator and any variable (except one) occurs at most twice. For these formulas we show that an infinite hierarchy $S_1\subseteq S_2\cdots$ exists such that we can test any formula from $S_i$ for falsifiability in time O(ni), where $n$ is the number of variables in the formula. We describe an algorithm that finds a falsifying assignment, if one exists. Furthermore we show that the falsifiability problem for $\bigcup_{i=1}^\infty S_i$ is NP-complete by reducing the SAT-Problem. In contrast to the hierarchy described by Gallo and Scutella for Boolean formulas in CNF, where the test for membership in the k-th level of the hierarchy needs time O(nk), our hierarchy permits a linear time membership test. Finally we show that $S_1$ is neither a sub- nor a superset of some commonly known classes of Boolean formulas, for which the SAT-Problem has linear time complexity (Horn formulas, 2-SAT, nested satisfiability).", } @TechReport{zpr95-188, author = "W. Hochst{\"a}ttler and H. Schindler", institution = mi, title = "Recognizing {P4}-extendible graphs in linear time", year = "1995", crindex = "57k,13,zpr95-188.ps.gz", keywords = "graph theory, linear time algorithms, modular tree, P4-extendible graphs; 05C85, 68Q20, 68Q25", annote = "In a recent series of articles B. Jamison and S. Olariu introduced three classes of graphs with simple P4-structure. The well-known data structure of a cotree of a P4-free graph generalizes to these classes. We give a linear time algorithm to compute the parse tree for P4-extendible graphs.", } @TechReport{zpr95-187, author = "B. Steckemetz", institution = mi, title = "Quality Control of Ready-made Food", year = "1995", crindex = "589k,8,zpr95-187.ps.gz", keywords = "image processing, quality control; 68U10", annote = "We present a system for a visual control of ready-made food based on image processing algorithms. Pictures are taken with a CCD camera and a frame-grabber at a rate of one per second. In the first processing level the relevant information is extracted via a recursive split-and-merge algorithm. Prototypes are applied to the obtained clusters to get probability values for each ingredient. In a final decision stage connected objects belonging to the same prototype are compared to get an optimal global classification.", } @InProceedings{zpr95-186, author = "M. Neschen", institution = mi, title = "Hierarchical Binary Vector Quantisation Classifiers for Handwritten Character Recognition", booktitle = "Mustererkennung 95, Bielefeld", series = "Informatik aktuell", editor = "G. Sagerer and S. Posch and F. Kummert", publisher = "Springer-Verlag", pages = "419--427", year = "1995", crindex = "60k,10,zpr95-186.ps.gz", keywords = "pattern recognition, vector quantization, embedded systems", annote = "We report on a hierarchical nearest-neighbor classifier algorithm which we conceived for the recognition of handwritten characters. Distances to all classes are used both as a decision criterion in the classification hierarchy and for generating class membership coefficients. These likelihood values can be easily integrated in a multi-agent cognitive environment. We introduce a new completely binary version of the k-means cluster algorithm and explain how a highly efficient implementation can be achieved using binary patterns. Performances for large character databases are presented.", } @InProceedings{zpr95-185, author = "M. Neschen", institution = "mi", title = "Vector Quantisation Classifiers for Handwritten Character Recognition", booktitle = "Parallel Programming and Applications Proc. of the ZEUS-95 Workshop, Linkoping, Schweden", publisher = "IOS Press, Netherlands", series = "Concurrent Systems Engineering Systems", volume = "45", editor = "P. Fritzson and L. Finmo", year = "1995", crindex = "67k,14,zpr95-185.ps.gz", annote = "The development of a pattern recognition architecture based on vector quantization techniques is presented which is applied to the recognition of handwritten bank forms. After an overview of nearest-neighbor classification and clustering, a fast completely binary version of the k-means algorithm is introduced and results for latge character databases are given. An integration of these methods in a multi-agent environment is discussed. Both the efficient implementation on general MIMD processors and a realization on a dedicated SIMD architecture are presented.", } @Article{zpr95-184, author = "C. De Simone and M. Diehl and M. J{\"u}nger and P. Mutzel and G. Reinelt and G. Rinaldi", institution = inf, title = "Exact ground states in spin glasses: New experimental results with a branch-and-cut algorithm", journal = "Journal of Statistical Physics", volume = "80", number = "1/2", pages = "487--496", year = "1995", crindex = "47k,12,zpr95-184.ps.gz", keywords = "branch-and-cut, spin glasses, ground states; 82D30; 90C", annote = "In this paper we study 2-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch-and-cut, the exact ground states of grids of sizes up to 100 times 100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20,000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determined a priori. Our ground state energy estimation at zero field is -1.317.", } @PhdThesis{zpr95-183, author = "K. Nagel", school = mi, title = "High-speed microsimulations of traffic flow", year = "1994", crindex = "1125k,201,zpr95-183.ps.gz", } @TechReport{zpr94-182, author = "R. Schrader and G. Wambach", institution = inf, title = "Integer polyhedra from supermodular functions on series-parallel posets", year = "1994", keywords = "supermodular functions, integer polyhedra, scheduling, series-parallel posets; 90C10, 90C27, 90B35, 52B40, 52B12", annote = "We define a class of integer polyhedra induced by supermodular functions on series-parallel posets. We show that permutahedra and generalized polymatroids are special instances of our approach.", } @Article{zpr94-181, author = "R. Schrader and G. Wambach", institution = inf, title = "The Setup Polyhedron of Series-Parallel Posets", journal = "Discrete Applied Mathematics", year = "1997", volume = "79", number = "1-3", pages = "213--221", keywords = "setups, integer polyhedra, scheduling, 0-1-polytopes, series-parallel posets; 90C10, 90C27, 90B35, 52B12", annote = "To every linear extension L of a poset P=(P,<) we associate a {0,1}-vector x = x(L) with xe = 1 if and only if e is preceded by a jump in L or e is the first element in L. Let $Q = \conv\{ x(L) | L \in L(P) \}$ be the convex hull of all incidence vectors of linear extensions of P. For the case of series-parallel posets we give a linear description of Q.", } @TechReport{zpr94-180, author = "J.-T. Pfenning and D. Roweth", title = "Shared Memory Programming on the Meiko {CS}-2", year = "1995", crindex = "87k,11,zpr94-180.ps.gz", annote = "An interesting feature of some recent parallel computers is the fact that the underlying transport mechanism behind the currently dominating message passing interfaces is based on a global address space model. By accessing this global address space directly most of the inherent delays for administering message buffers and queues can be avoided. Using this interface we have implemented a user level distributed shared memory layer using the virtual memory protection mechanisms of the operating system. The synchronisation required for maintaining the coherency of the memory is addressed by implementing a distributed shared lock which exploits the remote atomic store operations provided by the Meiko CS-2. This allows an asynchronous style of pogramming where the load is dynamically distributed over the nodes of a parallel partition.", } @Article{zpr94-179, author = "A. von Arnim and A. S. Schulz", institution = inf, title = "Facets of the generalized permutahedron of a poset", journal = "Discrete Applied Mathematics", note = "Scheduling at Villa Vignoni", volume = "72", number = "1-2", pages = "179--192", year = "1997", keywords = "poset, precedence relation, generalized permutahedron, single machine weighted flowtime scheduling, valid inequalities; 90B35, 52B12, 06A07", annote = "Given a poset P as a precedence relation on a set of jobs with processing time vector p, the generalized permutahedron $\text{perm}(P,p)$ of P is defined as the convex hull of all job completion time vectors corresponding to a linear extension of P. Thus, the generalized permutahedron allows for the single machine weighted flowtime scheduling problem to be formulated as a linear programming problem over $\text{perm}(P,p)$. Queyranne and Wang (1991) as well as von Arnim and Schrader (1997) gave a collection of valid inequalities for this polytope. Here we present a description of its geometric structure that depends on the series decomposition of the poset P, prove a dimension formula for $\text{perm}(P,p)$, and characterize the facet inducing inequalities under the known classes of valid inequalities.", } @Article{zpr94-178, author = "U. Faigle and S. P. Fekete and W. Hochst{\"a}ttler and W. Kern", institution = mi, journal = "Mathematical Programming", title = "The Nucleon of Cooperative Games and an Algorithm for Matching Games", year = "1998", volume = "83", series = "A", number = "2", pages = "195--211", crindex = "61k,20,zpr94-178.ps.gz", keywords = "cooperative game, core, nucleolus, nucleon, matching; 90C27, 90D12", annote = "The nucleon is introduced as a new allocation concept for non-negative cooperative n-person transferable utility games. The nucleon may be viewed as the multiplicative analogue of Schmeidler's nucleolus. It is shown that the nucleon of (not necessarily bipartite) matching games can be computed in polynomial time.", } @Article{zpr94-177, author = "C. Wieners", title = "A parallel Newton multigrid method for high order finite elements and its application on numerical existence proofs for elliptic boundary value equations", journal = "Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik", volume = "76", pages = "171--176", year = "1996", crindex = "68k,10,zpr94-177.ps.gz", keywords = "parallel multigrid, nonlinear elliptic boundary equations, error bounds, Bratu problem; 65N55, 65N30, 65Y05, 65N15", annote = "We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C2-Hermite-elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain verified bounds, these computations are realized in interval arithmetic. The application of the Newton-Kantorovich-theorem yields the existence of a solution and error bounds for the approximation. The method is implemented on a 256 processor transputer grid and tested for the Bratu problem $-\Delta u=\lambda\exp(u)$.", } @TechReport{zpr94-176, author = "N. Masbaum", institution = mi, title = "Simulation of Ostwald Ripening in Two Dimensions: Spatial and Nearest Neighbor Correlations", crindex = "107k,20,zpr94-176.ps.gz", annote = "Recent experimental results on late stage coarsening (Ostwald ripening) in two dimensions were reinvestigated by means of numerical simulation using the Cahn-Hilliard equation (model B). We determine the spatial particle-particle and charge-charge correlation functions according to the experimental results of Krichevsky and Stavans. We find that our numerical results correspond well with these experiments. We also investigate particle-particle correlations between nearest neighbors (defined by the Voronoi diagram of particles centroids) following the experiments of Seul, Morgan and Sire and compare our numerical results with their Maximum Entropy model of Ostwald ripening.", } @InProceedings{zpr94-175, author = "T. Gerz and U. Schumann and M. Strietzel", institution = mi, title = "Large Eddy Simulation turbulenter Str{\"o}mungen auf {MIMD}-Systemen", booktitle = "Parallele Datenverarbeitung aktuell: Parallelrechner - Grundlagen und Anwendungen", editor = "R. Flieger and R. Grebe", pages = "357", year = "1994", crindex = "66k,14,zpr94-175.ps.gz", annote = "Die Analyse turbulenter Str{\"o}mungen mit hohen Reynoldszahlen erfordert numerische Simulationen auf gro{\ss}en Gebieten mit sehr hoher Aufl{\"o}sung. Der hier dargestellte parallele Algorithmus basiert auf der L{\"o}sung der Navier-Stokes Gleichung f{\"u}r inkompressible Fluids mit einem finite Differenzen Ansatz zweiter Ordnung auf einem versetzt angeordneten (staggered) Gitter. Es wird ein neuer Algorithmus dargestellt mit dem die f{\"u}r die Berechnung der Druckkomponente wesentliche Poissongleichung parallel gel{\"o}st wird. Erste Ergebnisse und Speed-Ups des Poissonl{\"o}sers und eines kompletten Simulationslaufes auf dem Parsytec GCel-1024 des ZPR K{\"o}ln werden pr{\"a}sentiert.", } @TechReport{zpr94-174, author = "M. J{\"u}nger and V. Kaibel and S. Thienel", institution = inf, title = "Computing Delaunay-Triangulations in Manhatten and Maximum Metric", year = "1994", crindex = "118k,27,zpr94-174.ps.gz", keywords = "Delaunay triangulation, Voronoi diagram, Manhattan metric, Maximum metric", annote = "Delaunay-Triangulations (the duals of Voronoi Diagrams) are well known to be structures that contain a lot of neighborhood-information about a given (finite) set of points in the plane. Many algorithms rely on efficient procedures to compute them in practical applications, yet the textbook descriptions usually only treat the case of Euclidean metric. We modify one of the algorithms known for the Euclidean case (the incremental algorithm of Ohya, Iri, and Murota) to become suitable for a more general class of ``Delaunay Triangulations'' including those for the Manhattan and Maximum metrics. We give a detailed description of this algorithm that makes it (rather) easy to write a computer program for the calculation of Delaunay Triangulations for these metrics. We give computational results for our own implementation of the algorithm.", } @Article{zpr94-173, author = "A. Bachem and K. Nagel and M. Rickert", institution = mi, title = "Ultraschnelle mikroskopische Verkehrssimulationen", journal = "Parallele Datenverarbeitung aktuell: TAT '94", year = "1994", pages = "460--469", publisher = "IOS Press; Ohmsha", crindex = "321k,10,zpr94-173.ps.gz", annote = "``Verkehrschaos'' ist ein wohlbekannter Begriff der Umgangssprache, aber die wenigen Versuche, ihn auf eine wissenschaftliche Grundlage zu stellen, benutzen die Kontinuumsapproximation. Wir verwenden stattdessen einen zellularen Automaten, der f{\"u}r die recht hohe Granularit{\"a}t von Verkehr (individuelle Fahrzeuge) auf nat{\"u}rliche Weise geeignet erscheint. Unsere Simulationen laufen deutlich schneller als die anderer Mikrosimulationsprojekte. Wir zeigen, neben Performance-Ergebnissen, Resultate einer Simulation des gesamten Autobahnnetzes von Nordrhein-Westfalen, Ans{\"a}tze zur Kl{\"a}rung der Chaosfrage sowie Experimente zu Advanced-Traffic-Management-Ma{\ss}nahmen.", } @Article{zpr94-172, author = "M. Schreckenberg and A. Schadschneider and K. Nagel and N. Ito", institution = mi, title = "Discrete stochastic models for traffic flow", journal = "Physical Review E", volume = "51", number = "4", pages = "2939", year = "1995", crindex = "1121k,35,zpr94-172.ps.gz", annote = "We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs. density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.", } @Article{zpr94-171, author = "K. Nagel and M. Paczuski", institution = mi, title = "Emergent traffic jams", journal = "Physical Review E", volume = "51", pages = "2909", crindex = "836k,20,zpr94-171.ps.gz", annote = "We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic jams with a power law distribution $P(t) \sim t^{-3/2}$ of lifetimes, t. On varying the vehicle density in a closed system, this critical state separates lamellar and jammed regimes, and exhibits $1/f$ noise in the power spectrum. Using random walk arguments, in conjunction with a cascade equation, we develop a phenomenological theory that predicts the critical exponents for this transition and explains the self-organizing behavior. These predictions are consistent with all of our numerical results.", } @PhdThesis{zpr94-170, author = "M. Malich", school = mi, title = "Simulated-Trading - Ein paralleles Verfahren zur {L}{\"o}sung von kombinatorischen Optimierungsproblemen", series = "Informatik", publisher = "Shaker-Verlag", location = "Aachen", year = "1995", pages = "138", crindex = "334k,140,zpr94-170.ps.gz", keywords = "vehicle routing problem, heuristics, improvement heuristics, parallel computing; 90B05, 90C27, 65Y05", } @Article{zpr94-169, author = "M. G{\"u}rtler and R. Heesen", title = "Von Hamstern und anderen Tieren", journal = "Optionsscheinmagazin", pages = "56--59, 62--63", month = jul, year = "1995", crindex = "55k,11,zpr94-169.ps.gz", keywords = "option pricing, exotic options; 90A09", annote = "In letzter Zeit f{\"u}hrte der Einsatz von derivativen Finanzinnovationen h{\"a}ufig zu Verlusten durch Fehlspekulationen, die m{\"o}glicherweise auf fehlende Kenntnis der Investoren zur{\"u}ckzuf{\"u}hren sind. Gerade die immer mehr in Mode kommende Klasse der ``Exotic-options'' hat einen gro{\ss}en Erkl{\"a}rungsbedarf. Ziel dieses Beitrages ist es, dem Anleger exemplarisch anhand eines Digital-Optionsscheines und sogenannter Hamster-Optionsscheine die Bewertung von exotischen Optionen n{\"a}herzubringen.", } @TechReport{zpr94-168, author = "M. J{\"u}nger and P. Mutzel and T. Odenthal and M. Scharbrodt", institution = inf, title = "The Thickness of Graphs without {K}5-Minors", crindex = "73k,10,zpr94-168.ps.gz", keywords = "thickness, topological graph theory, k5-free graphs, decomposition theorem, crossing number, skewness, graph-minor, 2-sum, Delta-sum; 05C10, 05C85, 68R10, 90C27", annote = "The thickness problem on graphs NP-hard and only few results concerning this graph invariant are known. Using decomposition theorems of Wagner and Truemper, we show that the thickness of graphs without K5-minors is less than or equal to two. Therefore, the thickness of this class of graphs can be determined with a planarity testing algorithm in linear time.", } @InProceedings{zpr94-167, author = "A. Bachem and L. Bettmer and S. Ditzen and I. Windm{\"o}ller", booktitle = "Geld, Finanzwirtschaft, Banken und Versicherungen", institution = mi, pages = "755--761", title = "Simulationsmodelle f{\"u}r Bausparkollektive", volume = "Sonderdruck", year = "1993", crindex = "125k,7,zpr94-167.ps.gz", keywords = "; 90A09, 90A19, 90A20", } @Article{zpr94-166, author = "U. Faigle and S. P. Fekete and W. Hochst{\"a}ttler and W. Kern", institution = mi, title = "On the Complexity of Testing Membership in the Core of Min-cost Spanning Tree Games", journal = "International Journal of Game Theory", volume = "26", number = "3", pages = "361--366", year = "1997", publisher = "Physica-Verlag, Heidelberg", crindex = "34k,6,zpr94-166.ps.gz", keywords = "cooperative game, core, spanning tree, NP-completeness, X3C; 90C27, 90D12, 90C60, 90D43", annote = "Let N= {1,...,n} be a finite set of players and KN the complete graph on the node set $N\cup \{0\}$. Assume that the edges of KN have nonnegative weights and associate with each coalition $S \subseteq N$ of players as cost c(S) the weight of a minimal spanning tree on the node set $S \cup \{0\}$.
Using transformation from `Exact cover by 3-sets', which is one of the six basic NP-complete problems in the book of M. R. Garey and D. S. Johnson [`Computers and intractability. A guide to the theory of NP-completeness' (1979)] we exhibit the following problem to be NP-complete. Given the vector $x\in{\frak R}\sp N$ with x(N)= c(N) decide whether there exists a coalition S such that x(S)> c(S).", } @InProceedings{zpr94-165, author = "M. J{\"u}nger and P. Mutzel", institution = inf, title = "The Polyhedral Approach to the Maximum Planar Subgraph Problem: New Chances for Related Problems", booktitle = "Proceedings of the DIMACS International Workshop on Graph Drawing '94", location = "Princeton, New Jersey, USA", editor = "R. Tamassia and I. G. Tollis", pages = "119--130", publisher = "Springer-Verlag", series = "Lecture Notes in Computer Science", number = "894", year = "1995", crindex = "50k,12,zpr94-165.ps.gz", keywords = "planar augmentation, planarization, biconnectivity, graph drawing, polyhedral combinatorics, branch-and-cut; 90C10, 68R10, 05C10, 90C27", annote = "In M. J{\"u}nger and P. Mutzel [Algorithmica, 16 (1996)] we used a branch-and-cut algorithm in order to determine a maximum weight planar subgraph of a given graph. One of the motivations was to produce a nice drawing of a given graph by drawing the found maximum planar subgraph, and then augmenting this drawing by the removed edges. Our experiments indicate that drawing algorithms for planar graphs which require 2- or 3-connectivity, resp. degree-constraints, in addition to planarity often give ``nicer'' results. Thus we are led to the following problems:
(1) Find a maximum planar subgraph with maximum degree d in IN.
(2) Augment a planar graph to a k-connected planar graph.
(3) Find a maximum planar k-connected subgraph of a given k-connected graph.
(4) Given a graph G, which is not necessarily planar and not necessarily k-connected, determine a new graph H by removing r edges and adding a edges such that the new graph H is planar, spanning, k-connected, each node v has degree at most D(v) and r+a is minimum.

Problems (1), (2) and (3) have been discussed in the literature, we argue that a solution to the newly defined problem (4) is most useful for our goal. For all four problems we give a polyhedral formulation by defining different linear objective functions over the same polytope which is the intersection of the planar subgraph polytope, see M. J{\"u}nger and P. Mutzel [Proc. IPCO3 (1993)], the k-connected subgraph polytope M. Stoer [LNCS 1531 (1992)] and the degree-constrained subgraph polytope. We point out why we are confident that a branch-and-cut algorithm for the new problem will be an implementable and useful tool in automatic graph drawing.", } @Article{zpr94-164, author = "H. Mika and J.-T. Pfenning and E. Schmoetten", institution = mi, title = "Netzinstallation von Solaris 2.3 {\"u}ber Subnetzgrenzen hinweg", journal = "Offene Systeme", month = feb, note = "Springer-Verlag", number = "1", volume = "4", year = "1994", crindex = "83k,26,zpr94-164.ps.gz", annote = "Wer sich schon einmal mit der Betreuung und Pflege mehrerer Solaris Maschinen besch{\"a}ftigt hat, der wird den damit verbundenen Zeitaufwand erfahren haben, insbesondere wenn man den Anspruch hat, den Zustand der Maschinen m{\"o}glichst aktuell (In Hinblick auf Patches, neueste Software, etc.) und identisch zu halten. Neben diesen rein praktischen Aspekten macht man als Systembetreuer h{\"a}ufig eine Erfahrung, die stark an die Gesetze der Thermodynamik erinnert: Geht man von anf{\"a}nglich identisch installierten Maschinen aus, so wird man nach einem gewissen Zeitraum feststellen, da{\ss} sich die Maschinen in ihren Zust{\"a}nden immer mehr unterscheiden. (Ein stetiger Anstieg der Entropie im System Solaris Maschinen ist festzustellen.) Idealvorstellung w{\"a}re hingegen, da{\ss} sich jede Maschine in einem fest definierten Zustand befindet und da{\ss} alle, soweit m{\"o}glich, gleich konfiguriert sind.
Am ZPR existieren neben acht Sparcstation 10, mit Serverfunktionen, sieben SparcClassic und f{\"u}nf Sparcstation 5, die als Bildschirmarbeitspl{\"a}tze dienen. Ausgehend von dieser Tatsache und den oben angef{\"u}hrten {\"U}berlegungen besch{\"a}ftigten wir uns mit der M{\"o}glichkeit, diese Rechner via Netz zu installieren. Die Idee dabei war, eine einfache, schnelle und leicht und zentral konfigurierbare Installation durchzuf{\"u}hren, die ohne Interaktion m{\"o}glich ist und die anschlie{\ss}end die Maschinen betriebsbereit h{\"a}lt.
Das zugrunde liegende Konzept ist einfach: Man installiere eine Maschine unter Solaris 2.3, installiere darauf einen Installationsserver, konfiguriere die zu installierenden Clients und starte deren Installation. Die Umsetzung dieses Konzepts stellte jedoch einige Anforderungen an uns. Als auff{\"a}lligstes Problem erwies sich die Tatsache, da{\ss} eine Netzinstallation unter Solaris 2.3 im wesentlichen auf Subnetze begrenzt ist. Diese Beschr{\"a}nkung war f{\"u}r unseren Fall nicht akzeptabel. Das Ergebnis unserer Arbeit ist im folgenden Artikel exemplarisch an der Netzinstallation und der Konfiguration unserer Bildschirmarbeitspl{\"a}tze dargestellt. Dabei beschreibt der erste Teil die Realisierung einer Installation via Netz an sich, {\"u}ber Subnetzgrenzen hinweg. Der zweite Teil behandelt den konkreten Fall der Installation einer Maschine vom Typ {\tt dataless} unter Verwendung des Filesystemtyps {\sf CacheFS} f{\"u}r das Verzeichnis {\tt /usr}.", } @TechReport{zpr94-163, author = "K. Mehlhorn and P. Mutzel and S. N{\"a}her", institution = inf, title = "An Implementation of the Hopcroft and Tarjan Planarity Test and Embedding Algorithm", year = "1994", crindex = "191k,46,zpr94-163.ps.gz", keywords = "planar graphs, embeddings, topological embeddings, planarity testing, graph theory; 05C10, 05C85, 68R10", annote = "We describe an implementation of the Hopcroft and Tarjan planarity test and embedding algorithm. The program tests the planarity of the input graph and either constructs a combinatorial embedding (if the graph is planar) or exhibits a Kuratowski subgraph (if the graph is non-planar).", } @Article{zpr94-162, author = "K. Mehlhorn and P. Mutzel", institution = inf, title = "On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm", journal = "Algorithmica", volume = "16", number = "2", pages = "233--242", publisher = "Springer-Verlag, New York, Inc.", year = "1996", crindex = "53k,10,zpr94-162.ps.gz", keywords = "planar graphs, embeddings, topological embeddings, planarity testing, graph theory; 05C10, 05C85, 68R10", annote = "We give a detailed description of the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. The embedding phase runs in linear time. An implementation based on this paper can be found in [Mehlhorn, Mutzel, N{\"a}her, 1993].", } @TechReport{zpr94-161, author = "P. Mutzel", institution = inf, title = "s-Chorded Cycle Graphs and their Relation to the Planar Subgraph Polytope", year = "1994", keywords = "graph theory, maximum planar subgraph, planarization, planar subgraph polytope, facets, polyhedral combinatorics; 90C27, 90C10, 05C10, 68R10", } @TechReport{zpr94-160, author = "W. Hochst{\"a}ttler and S. Kromberg and C. Moll", institution = mi, title = "A new Linear Time Algorithm for Computing the Convex Hull of a Simple Polygon in the Plane", year = "1994", crindex = "58k,12,zpr94-160.ps.gz", keywords = "convex hull, linear time algorithms, simple polygon, planar geometry; 68U05, 51N20", annote = "The problem of determining the convex hull of a simple polygon has received a lot of attention in the early eighties.
The first linear time algorithm for this task proposed by Sklansky [IEEE Trans. Comput. 21 (1972)] was based on the simple idea of removing all left turns while moving around the polygon in clockwise orientation. This algorithm was shown to fail in some cases. Since then several correct, yet more complicated linear algorithms have been published and classes of polygons have been determined for which Sklansky's original algorithm can be used.
In our note we show how to mend Sklansky's Algorithm in a simple way and prove the correctness of the resulting algorithm. As an application we show how to compute a rectangle of smallest area containing a given simple polygon in linear time.", } @Article{zpr94-159, author = "M. B{\"o}hm and E. Speckenmeyer", institution = inf, title = "A Fast Parallel {SAT}-Solver - Efficient Workload Balancing", journal = "Annals of Mathematics and Artificial Intelligence", editor = "E. Boros and M. C. Golumbic", volume = "17", number = "3-4", pages = "381--400", year = "1996", crindex = "72k,15,zpr94-159.ps.gz", keywords = "; 68T15", annote = "We present a fast parallel SAT-solver on a message based MIMD machine. The input formula is dynamically divided into disjoint subformulas. Small subformulas are solved by a fast sequential SAT-solver running on every processor, which is based on the Davis-Putnam procedure with a special heuristic for variable selection. The algorithm uses optimized data structures to modify boolean formulas.
Additionally efficient workload balancing algorithms are used, to achieve a uniform distribution of workload among the processors.We consider the communication network topologies d-dimensional processor grid and linear processor array. Tests with up to 256 processors have shown very good efficiency-values (>0.95).", } @TechReport{zpr94-158, author = "M. J{\"u}nger and V. Kaibel and S. Thienel", institution = inf, title = "A Practical Method for Computing Correct Delaunay Triangulations in the Euclidian Metric", year = "1994", crindex = "87k,25,zpr94-158.ps.gz", keywords = "Delaunay triangulation, Voronoi diagram, Computational Geometry, Robust Algorithms", annote = "The correctness of many algorithms for computing Delaunay triangulations for the Euclidean Metric (as well as for several other problems in Computational Geometry) basically depends on the correct evaluation of the signs of certain arithmetical expressions with integer operands. Since the numbers to deal with often exceed the bounds up to which computers are able to calculate exactly, one has to employ expensive software arithmetic (``big integer packets'') to provide correctness in many cases.
We present a method to decide dynamically (i.e., for each evaluation occurring during a run of the used algorithm) if it is necessary to perform it by software arithmetic or if one can guarantee the correct evaluation when using a certain ``inexact'' hardware arithmetic, e.g., the floating point arithmetic of the used system. We apply this method to the computation of Delaunay triangulations and report about some computational results.", } @InProceedings{zpr94-157, author = "K. Nagel and S. Rasmussen", institution = mi, title = "Traffic at the Edge of Chaos", booktitle = "Artificial Life IV: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems", editor = "R. A. Brooks and P. Maes", pages = "222", publisher = "MIT Press", location = "Cambridge, MA", year = "1994", crindex = "2000k,15,zpr94-157.ps.gz", annote = "We use a very simple description of human driving behaviour to simulate traffic. The regime of maximum vehicle flow in a closed system shows near-critical behaviour, and as a result a sharp decrease of the predictability of travel time. Since Advanced Traffic Management Systems (ATMSs) tend to drive larger parts of the transportation system towards this regime of maximum flow, we argue that in consequence that the traffic system as a whole will be driven closer to criticality, thus making predictions much harder. A simulation of a siplified transportation network supports our argument.", } @InCollection{zpr94-156, author = "M. J{\"u}nger and G. Reinelt and S. Thienel", institution = inf, title = "Practical Problem Solving with Cutting Plane Algorithms in Combinatorial Optimization", booktitle = "Combinatorial optimization. Papers from the DIMACS special year. Papers from workshops held at DIMACS at Rutgers University", series = "DIMACS Series in Discrete Mathematics and Theoretical Computer Science", location = "New Brunswick, NJ, USA", editor = "W. Cook and L. Lovász and P. Seymour", volume = "20", pages = "111--152", year = "1995", crindex = "149k,45,zpr94-156.ps.gz", keywords = "cutting plane algorithms, branch-and-cut algorithms, parallelization; 90C27, 90C11, 65Y05, 65K05", annote = "Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch-and-bound framework. Implementations of such ``branch-and-cut'' algorithms are rather complicated in comparison to many purely combinatorial algorithms. The purpose of this article is to give an introduction to cutting plane algorithms from an implementor's point of view. Special emphasis is given to control and data structures used in practically successful implementations of branch-and-cut algorithms. We also address the issue of parallelization. Finally, we point out that in important applications branch-and-cut algorithms are not only able to produce optimal solutions but also approximations to the optimum with certified good quality in moderate computation times. We close with an overview of successful practical applications in the literature.", } @TechReport{zpr94-155, author = "F. Damm and F.-P. Heider and G. Wambach", institution = inf, title = "Factoring Integers above 100 Digits using Hypercube {MPQS}", crindex = "49k,14,zpr94-155.ps.gz", keywords = "Hypercube MPQS, Factorization; 11Y05", annote = "In this pape we report on further progress with the factorisation of integers using the MPQS algorithm on hypercubes and a MIMD parallel computer with 1024 T-805 processors. We were able to factorise a 101 digit number from the Cunningham list using only about 65 hours computing time. We give new details about the hypercube sieve initialisation procedure and describe the structure of the factor graph that saves a significant amount of computing time. At March 3rd, we finished the factorisation of a 104 digit composite.", } @Article{zpr94-154, author = "W. Hochst{\"a}ttler and S. Kromberg", institution = mi, title = "Adjoints and Duals of Matroids Linearly Representable over a Skew Field", journal = "Math. Scand.", volume = "78", number = "1", pages = "5--12", year = "1996", crindex = "45k,9,zpr94-154.ps.gz", keywords = "matroids, duality, adjoints, linear representation, skew field; 05B35, 12E15", annote = "Following an approach suggested by B. Lindstr{\"o}m we prove that the dual of a matroid representable over a skew field is itself representable over the same field. Along the same line we show that any matroid within this class has an adjoint. As an application we derive an adjoint for the dual of the Non-Pappus-Matroid. Furthermore, we reprove a result by Alfter and Hochst{\"a}ttler concerning the existence of an adjoint for a certain eight point configuration and show that this configuration is linearly representable over a field if and only if the field is skew.", } @Article{zpr94-153, author = "P. Bauer", institution = inf, title = "The Circuit Polytope: Facets", journal = "Math. Oper. Res.", volume = "22", number = "1", pages = "110--145", year = "1997", crindex = "192k,49,zpr94-153.ps.gz", keywords = "weighted girth problem, symmetric traveling salesman problem, circuit polytope, circuit cone, facets; 90C35, 90B06, 52B12, 90C10, 90C27", annote = "Given an undirected graph G=(V,E) and a costs c(e) attached to the edges of G, the weighted girth problem is to find a circuit in G having minimum total cost. This problem is in general NP-hard since the traveling salesman problem can be reduced to it.
A promising approach to hard combinatorial optimization problems is given by the so-called cutting plane methods. These involve linear programming techniques based on a partial description of the convex hull of the incidence vectors of possible solutions.
We consider the weighted girth problem in the case where G is the complete graph and study the facial structure of the circuit polytope and some related polyhedra. In the appendix we give complete characterizations of some small circuit polytopes.", } @InProceedings{zpr94-152, author = "J.-T. Pfenning", institution = mi, title = "Experiences with the Mether-{NFS} Virtual Shared Memory System", booktitle = "Proceedings of the High Performance Computing and Networking conference, Vol. 2: Networking and Tools", editor = "W. Gentzsch and U. Harms", series = "Lecture Notes in Computer Science", volume = "797", pages = "316--323", publisher = "Springer-Verlag", year = "1994", crindex = "96k,6,zpr94-152.ps.gz", annote = "Workstation clusters have recently attracted high interest as a technology providing supercomputer class performance at much lower price levels. The message passing programming model dominates the application development, despite the overhead and the complexity introduced by the explicitly coded synchronisation and data transfers. We give an introduction to the virtual shared memory programming model and report on the experiences with an implementation running on an FDDI network with 8 machines. We show that the direct coherence control mechanisms provided by the Mether-NFS system can be used to overcome the false sharing overhead caused by the coherency protocol. They provide an excellent tool for parallelizing programs using complex data structures with dynamic load balancing.", } @Article{zpr94-151, author = "J.-T. Pfenning and C. Moll", institution = mi, title = "Optimized communication patterns on workstation clusters", journal = "Parallel Computing", volume = "21", number = "3", pages = "373--388", month = mar, year = "1995", crindex = "389k,17,zpr94-151.ps.gz", keywords = "message passing, workstation cluster, communication optimization, PVM, FDDI, Dynamic loop scheduling algorithm, parallel efficiency; 68Q20, 68M10, 68M20", annote = "The limited communication bandwidth and high startup latencies of clustered workstations restrict their use to problems with sparse communication patterns or good concurrency between calculation and communication. First we describe our modifications to the popular PVM message passing library, and report on performance improvements using the PVM package on an FDDI-ring. Applications developed with a parallel communications architecture in mind perform poorly when ported to a message passing library running on workstations with sequential communication. In the second part, we present a dynamic loop scheduling algorithm for the data parallel programming model which optimizes the network usage on such clusters. As a proof of concept we have implemented a basic matrix multiplication and find a significant increase in parallel efficiency.", } @TechReport{zpr94-150, author = "B. Steckemetz and M. Wottawa", institution = mi, title = "An efficient parallel cluster-heuristic for large {TSP}s", year = "1994", crindex = "78k,10,zpr94-150.ps.gz", keywords = "traveling salesman problem, heuristics, parallel algorithms, message passing, Lin-Kernighan; 90B05, 90-08, 68R99, 90C27", annote = "We describe an improved clustering heuristic for the Eucledian Traveling Salesman Problem and its parallelization for a distributed memory machine. A geometric decomposition is used for the clustering-stage and special emphasis has been put on the computation of the global tour through the clusters. The heuristic solves problem instances up to 33,000 cities in a few minutes on the parallel machine, while the obtained tour is only a few percent longer than a tour generated by the sequential Lin-Kernighan-algorithm.", } @InProceedings{zpr94-149, author = "F. Damm and F.-P. Heider and G. Wambach", institution = inf, title = "{MIMD}-Factorisation on Hypercubes", booktitle = "Advances in Cryptology - Proceedings of EUROCRYPT '94, Workshop on the theory and application of cryptographic techniques", editor = "A. De Santis", location = "Perugia, Italy", series = "Lecture Notes in Computer Science", volume = "950", publisher = "Springer-Verlag", pages = "400--409", year = "1995", crindex = "52k,11,zpr94-149.ps.gz", keywords = "Hypercube MPQS, Factorization, MIMD Parallelisation; 68Q22, 11Y05, 94A60", annote = "This paper describes the development and implementation of the MPQS factoring algorithm using multiple hypercubes customised to a MIMD parallel computer. The computationally most expensive steps ran on a Parsytec machine consisting of 1024 Inmos T805 microprocessors. General 100 decimal digit numbers can be factored in 1-2 days.", } @TechReport{zpr93-148, institution = mi, title = "Jahresbericht 1992", } @Article{zpr93-147, author = "A. Srivastav and P. Stangier", institution = inf, title = "Algorithmic Chernoff-Hoeffding Inequalities in Integer Programming", journal = "Random Structures & Algorithms", volume = "8", number = "1", pages = "27--58", year = "1996", crindex = "114k,28,zpr93-147.ps.gz", keywords = "randomized algorithm, derandomization, approximation algorithm, integer programming, multicommodity flows, resource constrained scheduling; 60C05, 60E15, 68Q25, 90C10, 90C27, 90B35, 90C35", annote = "Proofs of classical Chernoff-Hoeffding bounds have been used to obtain polynomial-time implementations of Spencer's derandomization method of conditional probabilities on usual finite machine models: given m events whose complements are large deviations corresponding to weighted sums of n mutually independent Bernoulli trials, Raghavan's lattice approximation algorithm constructs for 0-1 weights and integer deviation terms in O(mn)-time a point for which all events hold.
For rational weighted sums of Bernoulli trials the lattice approximation algorithm or Spencer's hyperbolic cosine algorithm are deterministic procedures, but a polynomial-time implementation was not known.
We resolve this problem with an $O(mn^2\log \frac{mn}{\epsilon})$-time algorithm, whenever the probability that all events hold is at least $\epsilon > 0$. Since such algorithms simulate the proof of the underlying large deviation inequality in a constructive way, we call it the algorithmic version of the inequality. Applications to general packing integer programs and resource constrained scheduling result in tight and polynomial-time approximations algorithms.", } @InProceedings{zpr93-146, author = "A. Srivastav and P. Stangier", institution = inf, title = "Integer Multicommodity Flows with Reduced Demands", booktititle = "Algorithms -- ESA ´93, Proc. of the First Annual European Symposium", location = "Bad Honnef, Germany", editor = "T. Lengauer", series = "Lecture Notes in Computer Science", volume = "726", pages = "360--371", year = "1993", publisher = "Springer-Verlag", crindex = "65k,12,zpr93-146.ps.gz", keywords = "randomized algorithm, derandomization, integer programming, multicommodity flow; 60C05, 60E15, 68Q25, 90C35, 05C85, 68R10", annote = "Given a supply graph G=(V,E), a demand graph H=(T,D), edge capacities $c:E\mapsto \Nset$ and requests $r:D\mapsto \Nset$, we consider the problem of finding integer multiflows subject to c, r. Korach and Penn constructed approximate integer multiflows for planar graphs, but no results were known for the general case. Via derandomization we present a polynomial-time approximation algorithm. There are two cases:
(a) The main result is: For fractional solvable instances (G,H,c,r) and each $0 < \epsilon \leq\frac{9}{10}$ our algorithm finds in polynomial-time an integer multiflow subject to c, such that for all $d \in D$ the $d-$th flow value satisfies $f(d) \ge (1-\ep)r(d),$ provided that capacities and requests are not too small, i.e $c,r = \Omega (\frac{1}{\epsilon^2}\log(|E|+|D|))$. In particular, if $c,r \ge 36 \lceil \log 2(|E|+|D| +1) \rceil$ we have a strongly polynomial-time algorithm and the first ½-factor approximation.
(b) If the problem is not fractionally solvable we can reduce it to the case mentioned above decreasing the requests in an optimal way. This can be done by linear programming and the results of (a) apply.
The design and analysis of the algorithm require new techniques for randomized rounding as well as for derandomization. One key tool is an algorithmic version of the classical Angluin-Valiant inequality (a variant of the well known Chernoff-Hoeffding bound) estimating the tail of weighted sums of Bernoulli trials, which was not previously known and might be of independent interest in computational probability theory.
The significance of our rounding algorithm is emphasized by the fact that there is a rich combinatorial theory exhibiting many examples of fractionally solvable problems, but finding approximate integer solutions even for fractionally solvable problems is NP-hard as it is shown in this paper.", } @Article{zpr93-145, author = "M. J{\"u}nger and P. Mutzel", institution = inf, title = "Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools", journal = "Algorithmica", volume = "16", number = "1", pages = "33--59", publisher = "Springer-Verlag, New York, Inc.", year = "1996", crindex = "145k,20,zpr93-145.ps.gz", keywords = "maximum planar subgraph, planar subgraph polytope, facets, branch-and-cut, Planarization, Polyhedral Combinatorics, graph drawing; 90C10, 68R10, 05C10, 90C27", annote = "In automatic graph drawing a given graph has to be layed-out in the plane, usually according to a number of topological and aesthetic constraints. Nice drawings for sparse nonplanar graphs can be achieved by determining a maximum planar subgraph and augmenting an embedding of this graph. This approach appears to be of limited value in practice, because the maximum planar subgraph problem is NP-hard.
We attack the maximum planar subgraph problem with a branch-and-cut technique which gives us quite good and in many cases provably optimum solutions for sparse graphs and very dense graphs. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K5 or K3,3, turn out to define facets of this polytope. For cliques contained in G, the Euler inequalities turn out to be facet-defining for the planar subgraph polytope. Moreover we introduce the subdivision inequalities, V2k inequalities and flower inequalities all of which are facet-defining for the polytope. Furthermore, the composition of inequalities by 2-sums is investigated.
We also present computational experience with a branch-and-cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K5 or K3,3. These structures give us inequalities which are used as cutting planes.
Finally, we try to convince the reader that the computation of maximum planar subgraphs is indeed a practical tool for finding nice embeddings by applying this method to graphs taken from the literature.", } @TechReport{zpr93-144, author = "G. Wambach", institution = inf, title = "The True Minimum Distance of Some Narrow-Sense {BCH}-Codes of Length 255", year = "1993", crindex = "37k,7,zpr93-144.ps.gz", keywords = "Binary linear Codes, Minimum Distance, BCH Codes; 11T71", annote = "Using equivalent codes it is shown that the BCH-bound of the following narrow-sense BCH-codes already yields the true minimum distance: [255,87,53], [255,107,45], [255,115,43], [255,123,39], [255,131,37], [255,147,29], [255,163,25], [255,179,21]. For the remaining two narrow-sense BCH-codes of length 255 in the book of F.J. MacWilliams and N.J.A. Sloane [The theory of error-correcting codes (1977)] page 261, figure 9.1, whose true minimum distance is still unknown, upper bounds for the minimum distance are given which differ by at most two from the corresponding BCH-bounds.", } @Article{zpr93-143, author = "A. von Arnim and R. Schrader and Y. Wang", institution = inf, title = "The Permutahedron of {N}-sparse Posets", journal = "Mathematical Programming A", volume = "75", number = "1", series = "A", pages = "1--18", year = "1996", keywords = "Combinatorial optimization, Weighted completion time scheduling, Precedence constraints, Integer Polyhedra, series-parallel posets, greedy algorithm; 90C10, 90C27, 90B35, 52B12", annote = "The permutahedron of a poset is the convex hull of all incidence vectors of linear extensions. For the case of N-sparse posets in which any five elements induce at most one N we give a characterization of the permutahedron in terms of linear inequalities. This yields an LP-solution for minimizing the weighted mean completion time for jobs with unit processing times and N-sparse precedence constraints. We close with an extension of our approach to arbitrary processing times", } @TechReport{zpr93-142, author = "S. P. Fekete and W. R. Pulleyblank", institution = mi, title = "Backward Error Analysis for the Travelling Salesman Problem: Generalized Convexity", keywords = "error analysis, backward error analysis, Traveling Salesman Problem (TSP), convexity, polyhedral norm, geometry, computational geometry, polynomial algorithm", annote = "We examine the notion of Backward Error Analysis for the Travelling Salesman Problem. One property that establishes the optimality of a tour for a given set of vertices is generalized convexity. Geometrically speaking, we examine the question: How far is a given set of vertices from forming a convex arrangement?
There are two metrics involved in this question: The distance metric of the TSP defines the particular type of convexity that we have to consider. The second metric describes the error bounds around the tour vertices, i.e. the amount of perturbation we must apply to a given set to obtain a set that forms a convex arrangement.
We consider several combinations of distance metrics and error metrics. We show that it is easy to solve the question for L1 distances and $L_{\infty}$ errors and also address the question of L1 distances with L1 errors. Our results can be generalized to polygonal norms. (A polygonal norm $L_{\cal P}$ has a centrally symmetric convex 2k-gon as its unit ball.) For Euclidean distances, we show how it can be decided in polynomial time whether a given $L_{\cal P}$ error bound around each point is sufficient to transform a point set into a convex arrangement. This is closely related to the notion of convex stabbing: Does a given family of sets allow a convex curve that intersects them all?
The notion of convex stabbing was introduced by Tamir in 1987. Goodrich and Snoeyink have given a solution for the special case of a family of parallel line segments. Our result on $L_{\cal P}$ norms yields a polynomial solution for the case of a family of congruent convex polygons with a fixed number of vertices.
We conclude this paper by discussing difficulties arising from convex stabbing of disks.", } @Article{zpr93-141, author = "K. Nagel", institution = mi, title = "Life-Times of Simulated Traffic Jams", journal = "International Journal of Modern Physics C", number = "3", pages = "567", volume = "5", year = "1994", annote = "We study a model for freeway traffic which includes strong noise taking into account the fluctuations of individual driving behavior. The model shows emergent traffic jams with a self-similar appearance near the throughput maximum of the traffic. The lifetime distribution of these jams shows a short scaling regime, which gets considerably longer if one reduces the fluctuations when driving at maximum speed but leaves the fluctuations for slowing down or accelerating unchanged. The outflow from a traffic jam self-organizes into this state of maximum throughput.", } @InProceedings{zpr93-140, author = "K. Nagel", institution = mi, title = "Fast Low Fidelity Microsimulation of Vehicle Traffic on Supercomputers", booktitle = "Transportation Research Board, Meeting Jan. 1994 in Washington D.C.", crindex = "331k,18,zpr93-140.ps.gz", annote = "A set of very simple rules for driving behavior used to simulate roadway traffic gives realistic results. Because of its simplicity, it is easy to implement the model on supercomputers (vectorizing and parallel), where we have achieved real time limits of more than 4 million kilometers (or more than 53 million vehicle sec/sec). The model can be used for applications where both high simulation speed and individual vehicle resolution are needed. We use the model for extended statistical analysis to gain insight into traffic phenomena near capacity, and we discuss that this model is a good candidate for network routing applications.", } @Article{zpr93-139, author = "A. Bachem and W. Hochst{\"a}ttler and M. Malich", institution = mi, title = "The Simulated Trading Heuristic for Solving Vehicle Routing Problems", journal = "Discrete Applied Mathematics", publisher = "Elsevier", volume = "65", number = "1-3", year = "1996", pages = "47--72", crindex = "121k,29,zpr93-139.ps.gz", keywords = "vehicle routing problem, heuristics, improvement heuristics, parallel computing; 90B05, 90C27, 65Y05", annote = "We present an improvement heuristic for vehicle routing problems. The heuristic finds complex customer interchanges to improve an initial solution. Our approach is modular, thus it is easily adjusted to different side constraints such as time windows, backhauls and a heterogeneous vehicle fleet. The algorithm is well suited for parallelization. We report on a parallel implementation of the Simulated Trading heuristic on a cluster of workstations using PVM. The computational results were obtained using two sets of vehicle routing problems which differ in the presence of time windows. Our results show that Simulated Trading is better suited for problems with time windows.", } @TechReport{zpr93-138, author = "B. Gerards and W. Hochst{\"a}ttler", institution = mi, title = "Onion Skins in Oriented Matroid", year = "1993", crindex = "39k,3,zpr93-138.ps.gz", keywords = "oriented matroids, shellability, polyhedra; 05B35, 52B05, 52B40, 51H20", annote = "We generalize the following theorem to oriented matroids: Consider a polytope P and a facet F0 of P, let H denote the hyperplanes spanned by F0. Let d denote the diameter of the coskeleton of P. To each facet choose a defining inequality and let these set of inequalities $\Fscr$ be partitioned by the distance of the corresponding facets to F0 in the coskeleton of P into $\Fscr = \cup_{i=0}^d \Fscr_i$ . Let $\tilde P_i$ denote the polyhedron defined by the inequalities $\Fscr_i$ and set $P_i :=\tilde P_i \cup H$. Then for all $iT und das L{\"o}sen eines Gleichungssystems ADAT * x = b, auf bis zu 32 Prozessoren verteilt werden. Da die ausgegliederten Operationen bis zu 96\% der sequentiellen Rechenzeit ben{\"o}tigen, erreichen wir durch diese Vorgehensweise eine Effizienz von bis zu 75\%. Die parallelen Berechnungen werden dabei von einem am Mathematischen Institut der Universit{\"a}t zu K{\"o}ln entwickelten Software-Packet (CARO) {\"u}bernommen, welches f{\"u}r eine gro{\ss}e Zahl von Standard-Anwendungen sehr effiziente Algorithmen und einfache Schnittstellen zur Verf{\"u}gung stellt. Die Arbeiten wurden auf einem Multicluster 2 der Firma Parsytec mit 32 T800 Transputern unter dem Betriebssystem HELIOS durchgef{\"u}hrt.", } @InProceedings{zpr93-128, author = "M. J{\"u}nger and P. Mutzel", institution = inf, title = "Solving the Maximum Weight Planar Subgraph Problem by Branch-and-Cut", booktitle = "Proceedings of the 3rd IPCO Conference (Integer Programming and Combinatorial Optimization), Erice", editor = "G. Rinaldi and L. Wolsey", pages = "479--492", year = "1993", crindex = "91k,13,zpr92-128.ps.gz", keywords = "Maximum planar subgraph, planar subgraph polytope, facets, branch-and-cut, planarization, polyhedral combinatorics, graph drawing; 90C10, 68R10, 05C10, 90C27", annote = "In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K5 or K3,3, turn out to define facets of this polytope.
We also present computational experience with a branch-and-cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K5 or K3,3. These structures give us inequalities which are used as cutting planes.", } @TechReport{zpr92-127, author = "W. Hochst{\"a}ttler and S. Kromberg and C. Moll", institution = mi, title = "A Simple Proof of the Blossom Expansion Lemma", year = "1992", crindex = "22k,1,zpr92-127.ps.gz", keywords = "Matching, Blossom Algorithm; 05C70", annote = "In the proof of the correctness of Edmonds' Blossom-Algorithm one implication of the equivalence of the existence of an augmenting path in the shrinked graph and the original graph is usually done by a lengthy case checking. We give a - better teachable - short proof. We assume familiarity with the blossom algorithm and matching theory.", } @TechReport{zpr92-126, author = "W. Hochst{\"a}ttler", institution = mi, title = "A Non-Visiting Path, Nested Cones and Onions Skins", year = "1992", crindex = "53k,8,zpr92-126.ps.gz", keywords = "oriented matroids, polyhedra, polarity; 05B35, 52B05, 52B40", annote = "We prove that the skeleton graph of a cell of an oriented matroid is still connected, if we delete all nodes adjacent to one facet. As an application we solve a problem stated by T. Terlaky.", } @InProceedings{zpr92-125, author = "A. Bachem and W. Hochst{\"a}ttler and M. Malich", title = "Simulated Trading - {A} New Parallel Approach For Solving Vehicle Routing Problems", booktitle = "Parallel Computing: Trends and Applications: Proceedings of the International Conference ParCo93, Grenoble, France, 7--10 September 1993", editor = "G. R. Joubert and D. Trystram and F. J. Peters and D. J. Evans", pages = "471--475", series = "Advances in Parallel Computing", volume = "9", publisher = "North-Holland", year = "1994", crindex = "29k,6,zpr92-125.ps.gz", keywords = "vehicle routing problem, heuristics, improvement heuristics, parallel computing; 90B05, 90C27", annote = "We present a parallel improvement heuristic for solving vehicle routing problems with additional constraints. The algorithm was implemented on a parallel transputer machine and on a cluster of workstations using PVM. The computational results obtained with sequential and parallel Simulated Trading show that our approach is superior compared to all heuristics known to the authors by now.", } @Article{zpr92-124, author = "A. von Arnim and C. de la Higuera", institution = inf, title = "Computing the jump number on semi-orders is polynomial", journal = "Discrete Applied Mathematics", volume = "51", number = "1-2", pages = "219--232", year = "1994", keywords = "polynomial-time algorithm, interval orders, jump number, semi-order; 06A07, 68Q25", annote = "Semi-orders from a subclass of interval orders: they can be represented as sets of intervals of a given length. We first prove that semi-orders can be partitioned by serialization (or series decomposition) without loss of the jump number aspect. On non-serializable semi-orders all linear extensions contain never more than two consecutive bumps (maximal chains of length at most 3). We then give a ``divide-and-conquer'' argument proving that to solve this case all we need is to be able to compute the number of maximal chains of length at least 2. This can also be dealt with in polynomial time, allowing us to claim that computing the jump number is polynomial on semi-orders.", } @Article{zpr92-123, author = "A. Srivastav and P. Stangier", institution = inf, title = "Weighted Fractional and Integral k-Matching in Hypergraphs", journal = "Discrete Applied Mathematics", volume = "57", number = "2-3", pages = "255--269", year = "1995", crindex = "66k,13,zpr92-123.ps.gz", keywords = "hypergraph matching, integer and linear programming, randomized algorithm, derandomization; 05B40, 68Q25, 68R05", annote = "We consider the problem of finding polynomial-time approximations of maximal weighted k-matchings in a hypergraph and investigate the relationship between the integral and fractional maxima of the corresponding 0-1 integer linear program and its LP-relaxation. We extend results of Raghavan, who gave a deterministic approximation algorithm for unweighted k-matching, to the weighted case and compare the so obtained lower bound for the ratio of the integer and fractional maximum with a lower bound of Aharoni, Erd{\"o}s and Linial.", } @TechReport{zpr92-122, author = "A. Srivastav and P. Stangier", institution = inf, title = "On Derandomized Approximation Algorithms", year = "1992", crindex = "101k,32,zpr92-122.ps.gz", keywords = "combinatorial discrepancies, randomized algorithm, derandomization, discrete martingales; 05B40, 60G42, 68Q25, 68R05", annote = "With the design of powerful randomized algorithms the transformation of a randomized algorithm or probabilistic existence result for combinatorial problems into an efficient deterministic algorithm (called derandomization) became an important issue in algorithmic discrete mathematics. In the last years several interesting examples of derandomization have been published, like discrepancy in hypergraph colouring, packing integer programs and an algorithmic version of the Lovász-Local-Lemma. In this paper the derandomization method of conditional probabilities of Raghavan/Spencer is extended using discrete martingales. As a main result pessimistic estimators are constructed for combinatorial approximation problems involving non-linear objective functions with bounded martingale differences. The theory gives polynomial-time algorithms for the linear and quadratic lattice approximation problem and a quadratic variant of the matrix balancing problem extending results of Spencer, Beck/Fiala and Raghavan. Finally a probabilistic existence result of Erd{\"o}s on the average graph bisection is transformed into a deterministic algorithm.", } @InProceedings{zpr92-121, author = "A. Bachem and M. Strietzel", institution = mi, title = "Eine parallele Implementierung des Karmarkar-Verfahrens", booktitle = "Proceedings of the Transputer-Anwender-Treffen TAT '92", year = "1992", crindex = "43k,10,zpr92-121.ps.gz", annote = "Es wird eine parallele Version des Karmarkar Verfahrens zur Linearen Programmierung dargestellt, die auf einem Multicluster 2 implementiert wurde. Der Hauptaufwand liegt dabei in der L{\"o}sung eines Gleichungssystems der Form ADAT * x = b, was mit einer Cholesky-Zerlegung f{\"u}r d{\"u}nnbesetzte Matrizen erfolgt. Die Faktorisierung von ADAT f{\"u}llt bis zu 98\% der Laufzeit aus. Sie wurde mit einem Fan-In Algorithmus auf 2, 4 und 8 Worker Prozessoren verteilt. Um eine gleichm{\"a}{\ss}ige Lastverteilung zu erreichen, ist ein Mapping-Verfahren installiert worden, welches die Struktur des Cholesky-Faktors graphentheoretisch analysiert.", } @InCollection{zpr92-120, author = "B. Feldman and K. Nagel", institution = mi, title = "Lattice Games with Strategic Takeover", booktitle = "Lectures in Complex Systems, Papers from the summer school held in Santa Fe, NM, USA, 1992", editor = "D Stein and L. Nadel", pages = "603--614", series = "St. Fe Inst. Stud. Sci. Complexity", publisher = "Addison-Wesley", volume = "5", year = "1993", crindex = "181k,21,zpr92-120.ps.gz", keywords = "iterated prisoner's dilemma, agents on a lattice; 90D20, 90D10, 90D40", annote = "This contribution explores a topic of interest in a surprising number of physical and social sciences, the iterated prisoner's dilemma game. We use this game to construct a simple model of strategic interaction on a lattice. The basic game describes two prisoners, accused of having committed a crime together, who are unable to communicate. Each is told that, if he confesses (defection), he will get a lighter sentence, but that he will receive a very heavy sentence if he does not confess and the other prisoner does. However, if neither confesses (cooperation), each receives a medium sentence.
Both prisoners defecting is the only equilibrium in the game because they cannot make a binding agreement to cooperate. In the basic game theoretic analysis, cooperation can be sustained only by the indefinite repetition (iteration) of the game. The expected future benefits of cooperation must be greater than defection, and cooperation is difficult to sustain.
The principal variation in our work is that we arrange agents on a lattice and have them play the same strategy simultaneously, but only against their immediate neighbors. The secondary variation in our work is that in most of our runs we allow payoffs to accumulate and, if an agent goes bankrupt, he is ``taken over'' by his most successful neighbor and adopts her strategy. Thus successful strategies propagate spatially, in a simple representation of diffusion through economic and social networks. In our study there are four important factors to consider:
(1) how many iterations an agent can remember and what he can remember;
(2) the relative advantage to noncooperation;
(3) the degree of ``selection pressure''; and
(4) the geometry of the lattice.

In some of our runs we introduce a low rate of mutation in strategies which gives our work some of the quality of genetic algorithm methods. The work reported here focuses primarily on the effects of selection pressure and variations in the incentive to defect.
It is rare that two players would play only against each other or that all agents would play all other agents in realistic economic situations. Typically, we expect a network of connections between agents. One approach to studying such networks is to model them as spatial behavior on a d-dimensional lattice. Axelrod already reports on experiments similar to ours on a lattice, but, in his work, agents play their neighbors separately. Most studies of evolutionary processes assume random or uniform matching. Here we allow the diffusion of strategies to take place, but do not make prior assumptions as to how complete ``mixing'' will be.", } @InProceedings{zpr92-119, author = "A. Bachem and M. Wottawa", institution = mi, title = "Parallelisierung von Heuristiken f{\"u}r gro{\ss}e Traveling Salesman Probleme", booktitle = "Parallele Datenverarbeitung mit dem Transputer (TAT'92)", editor = "Grebe and Baumann", publisher = "Springer-Verlag", series = "Reihe Informatik Aktuell", year = "1992", crindex = "121k,12p,zpr92-119.ps.gz", keywords = "traveling salesman problem, parallel algorithms, heuristics; 90B05, 90-08, 68R99, 90C27", annote = "Wir werden parallele Versionen von TSP-Heuristiken vorstellen, die in der Praxis sowohl durch ihr Laufzeitverhalten als auch durch die Qualit{\"a}t der von ihnen generierten L{\"o}sungen {\"u}berzeugen: eine parallele Insert-Heuristik, Lin-Kernighan-Verbesserungsheuristik sowie ein Clusterungsverfahren. Die beschriebenen Techniken der Parallelisierung (Data-Parallelism, Job-Parallelism, geometrische Aufteilung) lassen sich analog auch auf andere Algorithmen anwenden.", } @Article{zpr92-118, author = "W. Hochst{\"a}ttler", institution = mi, title = "Nested Cones and Onion Skins", journal = "Applied Mathematics Letters", volume = "6", number = "2", pages = "67--69", year = "1993", crindex = "46k,5,zpr92-118.ps.gz", keywords = "oriented matroids, polyhedra, polarity; 05B35, 52B05, 52B40, 51H20", annote = "We give a short geometric proof of a ``nested cones'' theorem answering a question asked by T. Terlaky in the Matroid Workshop of ARIDAM VII in the RUTCOR 1992. Exploiting polarity yields a theorem on ``onion skins''.", } @PhdThesis{zpr92-117, author = "W. Hochst{\"a}ttler", institution = mi, title = "Seitenfl{\"a}chenverb{\"a}nde orientierter Matroide", year = "1992", crindex = "244k,91,zpr92-117.ps.gz", keywords = "oriented matroids, face lattice, polyhedra, polarity, shellability, arrangement of hyperplanes, linear programming; 05B35, 06A08, 06B30, 51H20, 52B05, 52B30, 52B40, 68U05, 90C05", annote = "In dieser Arbeit wollen wir uns vor allem mit verbandstheoretischen Zusammenh{\"a}ngen zwischen Matroiden und orientierten Matroiden besch{\"a}ftigen. Nach den Kapiteln, die Problemstellungen untersuchen, die nicht direkt aus der Anwendung motiviert sind, m{\"o}chten wir anhand zweier Beispiele aufzeigen, da{\ss} es sehr wohl gelingt, mit Hilfe der Abstraktion auf orientierte Matroide anwendungsorientierte Probleme zu l{\"o}sen.

Die Arbeit ist wie folgt gegliedert:
Mit dem zweiten Kapitel wollen wir dem Leser das Nachschlagen in diversen Standardwerken ersparen und die verwendeten Notationen einf{\"u}hren.
Im darauffolgenden Kapitel wollen wir die f{\"u}r diese Arbeit n{\"o}tigen Grundlagen der (orientierten) Matroidtheorie entwickeln. Mit einigen Beweisen m{\"o}chten wir aufzeigen, da{\ss} manche Sachverhalte in orientierten Matroiden leichter zu verifizieren sind, wenn man die zugrundeliegende unorientierte Struktur ausn{\"u}tzt.
Die Thematik des vierten Kapitels war f{\"u}r uns der Einstiegspunkt in die Arbeit mit orientierten Matroiden. Wir hatten die bis dahin unver{\"o}ffentlichte Sch{\"a}lbarkeit der orientierten Matroide wiederentdeckt Die in jener Arbeit benutzten Definitionen sind aber umst{\"a}ndlich und unklassisch. Deshalb halten wir uns in dieser Arbeit in der Darstellung weitestgehend an den von A. Bj{\"o}rner vorgeschlagenen Zugang. Nach Bereitstellung der n{\"o}tigsten Grundlagen aus der algebraischen Topologie werden wir im Laufe dieses Kapitels den Beweis des Darstellungssatzes (Folkmann, Lawrence, Edmonds, Mandel) orientierter Matroide skizzieren.
Im n{\"a}chsten Teil der Arbeit entwickeln wir eine verbandstheoretische Axiomatisierung orientierter Matroide. Allerdings handelt es sich hierbei nicht um eine Charakterisierung mittels Verbandsgleichungen. Vielmehr nutzen wir die einfache Charakterisierung geometrischer Verb{\"a}nde (Matroide) mittels Verbandsgleichungen aus und studieren, wann eine Abbildung eines Verbands in einen geometrischen Verband die Nullabbildung eines orientierten Matroids ist.
Mit Hilfe dieser Charakterisierung geben wir im sechsten Kapitel zun{\"a}chst einen neuen Beweis f{\"u}r die Axiomatisierung orientierter Matroide als Sph{\"a}rensysteme nach Edmonds-Mandel. Hierbei verzichten wir direkt auf das dritte (Ball-) Axiom, dessen Redundanz Mandel zeigen konnte. Im darauffolgenden Paragraphen schw{\"a}chen wir das zweite Axiom ab, ohne Struktur zu verlieren. Die so gewonnene Charakterisierung l{\"a}{\ss}t sich nun zu einer, der oben erw{\"a}hnten {\"a}hnlichen, weiteren verbandstheoretischen Charakterisierung nutzen.
In den abschlie{\ss}enden beiden Kapiteln geben wir zwei Beispiele f{\"u}r Anwendungen der Theorie orientierter Matroide. Zun{\"a}chst gewinnen wir einen kleinen Satz aus der Polyedertheorie, mit dessen Hilfe wir ein Problem l{\"o}sen konnten, das im Matroidworkshop der ARIDAM VII vorgestellt wurde.
Die zweite Anwendung stammt aus dem Bereich der Computational Geometry. Hier gelang es uns, den Beweis des schwachen Zonensatzes f{\"u}r Pseudo-Hyperebenen Arrangements vom 3-dimensionalen auf beliebige Dimension zu verallgemeinern. Daf{\"u}r skizzieren wir zun{\"a}chst, wie man aus einem Pseudo-Hyperebenen Arrangement ein orientiertes Matroid erh{\"a}lt. (Uns ist daf{\"u}r kein ausgef{\"u}hrter Beweis bekannt.)", } @TechReport{zpr92-116, author = "A. Bachem and W. Hochst{\"a}ttler and W. Wenzel", institution = mi, title = "Sensitivity Analysis for General Equilibrium Problems", year = "1992", crindex = "57k,13,zpr92-116.ps.gz", keywords = "general economic equilibrium, sensitivity analysis, variational inequalities; 90A15, 49K40, 58E35", annote = "In this paper we give an elementary introduction into the theory of variational inequalities and their application to general equilibrium analysis. Furthermore we incorporate some results on sensitivity analysis of variational inequalities on polyhedral sets.", } @Article{zpr92-115, author = "K. Nagel and M. Schreckenberg", institution = mi, title = "A cellular automaton model for freeway traffic", journal = "Journal de Physique I", number = "2", pages = "2221", year = "1992", keywords = "transportation, traffic flow, celluar automata;", } @Article{zpr92-114, author = "M. J{\"u}nger and G. Reinelt and S. Thienel", institution = inf, title = "Provably good solutions for the traveling salesman problem", journal = zor, volume = "40", number = "2", pages = "183--217", year = "1994", crindex = "166k,45,zpr92-114.ps.gz", keywords = "true optimum solutions; traveling salesman problem; 90C35, 90C27", annote = "The determination of true optimum solutions of combinatorial optimization problems is seldomly required in practical applications. The majority of users of optimization software would be satisfied with solutions of guaranteed quality in the sense that it can be proven that the given solution is at most a few percent off an optimum solution. This paper presents a general framework for practical problem solving with emphasis on this aspect. A detailed discussion along with a report about extensive computational experiments is given for the traveling salesman problem.", } @InCollection{zpr92-113, author = "M. J{\"u}nger and G. Reinelt and G. Rinaldi", institution = inf, title = "The Traveling Salesman Problem", booktitle = "Network Models, Handbook on Operations Research and Management Science", editor = "M. O. Ball and T. Magnanti and C. L. Monma and G. Nemhauser", publisher = "Elsevier, North Holland", volume = "7", pages = "225--230", year = "1995", keywords = "traveling salesman; 90C35, 90C27, 90-02", annote = "This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling s problemalesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances.
Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances.", } @InProceedings{zpr92-112, author = "W. Hochst{\"a}ttler and M. Loebl and C. Moll", institution = mi, title = "Generating Convex Polyominoes at Random", booktitle = "Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993)", journal = "Discrete Mathematics", volume = "153", number = "1-3", pages = "165--176", year = "1996", crindex = "53k,13,zpr92-112.ps.gz", keywords = "polyomino, enumeration, algorithm; 05B50, 68R15", annote = "We give a new recursion formula for the number of convex polyominoes with fixed perimeter. From this we derive a bijection between an intervall of natural numbers and the polyominoes of given perimeter. This provides a possibility to generate such polyominoes at random in polynomial time. Our method also applies for fixed area and even when fixing both, perimeter and area. In the second part of the paper we present a simple linear time probabilistic algorithm which uniformly generates convex polyominoes of given perimeter with asymptotic probability 0.5.", } @InCollection{zpr92-111, author = "M. J{\"u}nger and W. R. Pulleyblank", institution = mi, title = "Geometric Duality and Combinatorial Optimization", booktitle = "Jahrbuch {\"U}berblicke Mathematik", publisher = "Vieweg Verlag", editor = "Chatterji et al.", pages = "1--24", year = "1993", keywords = "geometric duality, geometric combinatorial programming, duality; 90C27, 52C15, 49N15", annote = "Many combinatorial optimization problems have natural geometric versions, that is, versions in which the objects are points or lines in Euclidean space and the cost function is given by a planar metric. For example, a Euclidean Traveling Salesman Problem is specified by giving n points in the plane, and then requiring the construction of a tour with minimum Euclidean (L2) length passing through these points.
A problem encountered in VLSI design is that of constructing minimum weight Steiner trees on a set of n points in the plane, for which the edge lengths are given by the Manhattan, or L1, metric. For many such problems there are natural ``dual'' problems. These are geometric problems, usually involving optimally packing some shape in the plane, with the property that any feasible solution to the dual problem provides a bound on the optimum solution to the original problem. Moreover, in some cases, the ``best'' such bound is tight; its value equals that of the optimum solution. We describe several such optimization problems and their geometric duals. We also discuss the solvability of these problems.", } @Article{zpr92-110, author = "W. Hochst{\"a}ttler", institution = mi, title = "A Note on the Weak-Zone-Theorem", journal = "Congressus Numerantium", volume = "98", pages = "95--103", year = "1993", crindex = "49k,10,zpr92-110.ps.gz", keywords = "computational geometry, arrangement of pseudo hyperplanes, oriented matroids, linear programming, duality; 05B35, 68U05, 90C05", annote = "In a recent paper J. Matousek gave a simple proof of a weak form of the zone theorem which estimates the number of facets in the zone of a (Pseudo-)Hyperplane arrangement. In the Pseudo-Case he gave the full proof only for the 3-dimensional case. In this short note we want to point out, that his proof in fact uses Linear Programming duality and so can be generalized easily to all dimensions using duality of Oriented Matroids.", } @Article{zpr92-109, author = "M. Alfter and W. Hochst{\"a}ttler", institution = mi, title = "On Pseudomodular Matroids and Adjoints", journal = "Discrete Applied Mathematics", note = "ARIDAM VI and VII (New Brunswick, NJ, 1991/1992)", volume = "60", number = "1-3", pages = "3--11", year = "1995", crindex = "48k,10,zpr92-109.ps.gz", keywords = "matroids, adjoints, pseudomodularity; 05B35, 06C10", annote = "There are two concepts of duality in combinatorial geometry. A set theoretical one, generalizing the structure of two orthocomplementary vector spaces and a lattice theoretical concept of an adjoint, that mimics duality between points and hyperplanes. The latter - usually called polarity - seems to make sense almost only in the linear case. In fact the only non-linear combinatorial geometries known to admit an adjoint were of rank 3. Moreover, N. E. Mnëv conjectured that in higher ranks there would exist no non-linear oriented matroid that has an oriented adjoint. At least with unoriented matroids this is not true. In this paper we present a class of rank 4 matroids with adjoint including a non-linear example.", } @Article{zpr92-108, author = "M. J{\"u}nger and G. Reinelt", institution = mi, title = "Schnittebenenverfahren in der Kombinatorischen Optimierung", journal = "GAMM-Mitteilungen", volume = "15", number = "2", year = "1992", pages = "120--134", crindex = "58k,15,zpr92-108.ps.gz", keywords = "cutting plane methods; 90C27, 90-02, 52B12", annote = "Bei der L{\"o}sung anwendungsrelevanter Fragestellungen in Mathematik, Informatik, den Naturwissenschaften und Wirtschaftswissenschaften, sowie in der industriellen Praxis, die als kombinatorische Optimierungsprobleme formuliert werden k{\"o}nnen, haben sich die auf Polyedertheorie basierenden Schnittebenenverfahren als sehr leistungsf{\"a}hig erwiesen. In vielen F{\"a}llen ist der Einsatz von Schnittebenenverfahren die derzeit einzige zur Verf{\"u}gung stehende Technik zur L{\"o}sung praxisrelevanter Gr{\"o}{\ss}enordnungen der auftretenden Probleminstanzen. In diesem {\"U}bersichtsartikel werden Theorie und Praxis von Schnittebenenverfahren zusammenfassend skizziert.", } @TechReport{zpr92-107, author = "P. Mutzel", institution = inf, title = "A fast 0(n) Embedding Algorithm, based on the Hopcroft-Tarjan Planary Test", year = "1992", crindex = "128k,26,zpr92-107.ps.gz", keywords = "planar graphs, embeddings, planarity testing, graph theory, topological embeddings; 05C10, 05C85, 68R10", annote = "The embedding problem for a planar undirected graph G = (V,E) consists of constructing adjacency lists A(v) for each node v in V, in which all the neighbors of v appear in clockwise order with respect to a planar drawing of G. Such a set of adjacency lists is called a (combinatorial) embedding of G.
Chiba presented a linear time algorithm based on the `vertex-addition' planarity testing algorithm of Lempel, Even and Cederbaum using a PQ-tree. It is very complicated to implement this data structure. He also pointed out that it is fairly complicated to modify the linear `path-addition' planarity testing algorithm of Hopcroft and Tarjan, such that it produces an embedding.
We present a straightforward extension of the Hopcroft and Tarjan planarity testing algorithm which is easy to implement. Our method runs in linear time and performs very efficiently in practice.", } @TechReport{zpr92-106, author = "M. Malich", institution = mi, title = "Transputer und ihre Architektur - Eine {\"U}bersicht", year = "1992", crindex = "83k,17,zpr92-106.ps.gz", annote = "In diesem Aufsatz werden die grundlegenden Eigenschaften, wowie die Vor- und Nachteile des Transputerparallelrechners erl{\"a}utert und Hinweise zur Programmierung und Benutzung des Helios-Betriebssystems gegeben. Nach einer kurzen Beschreibung der Hardware erl{\"a}utern wir die Netzwerktopologie eines Transputerrechners. Eine kurze Beschreibung des Helios-Betriebssystems wird im dritten Abschnitt gegeben. Anschlie{\"s}end erfolgt der Einstieg in den Bereich der Kommunikation zwischen Transputerprozessoren innerhalb eines Netzwerks. Im letzten Teil wird speziell auf die Benutzung von Prozessoren und Semaphoren eingegangen, die von der Hardware des Prozessors unterst{\"u}tzt werden.", } @Article{zpr91-105, author = "M. J{\"u}nger and W. R. Pulleyblank", institution = inf, title = "New primal and dual Matching heuristics", journal = "Algorithmica", volume = "13", number = "4", pages = "357--380", publisher = "Springer-Verlag, New York, Inc.", year = "1995", keywords = "heuristic, minimum-cost spanning tree, moat widths; 68Q20, 68R10", annote = "We describe a new heuristic for constructing a minimum cost perfect matching designed for problems on complete graphs whose cost functions satisfy the triangle inequality (e.g., Euclidean problems). The running time for an n node problem is O(n log n) after a minimum cost spanning tree is constructed. We also describe a procedure which, added to Kruskal's algorithm, produces a lower bound on the size of any perfect matching. This bound is based on a dual problem which has the following geometric interpretation for Euclidean problems: Pack nonoverlapping discs centered at the nodes and moats surrounding odd sets of nodes so as to maximize the sum of the disc radii and moat widths.", } @Article{zpr91-104, author = "M. Middendorf", institution = mi, title = "Symmetric Matroids and Connectivity Properties of Graphs", journal = "European Journal of Combinatorics", publisher = "Academic Press", crindex = "40k,12,zpr91-104.ps.gz", annote = "A symmetric matroid is a matroid defined on the edge-set of some countably infinite complete graph K in a way that ranks of finite subgraphs of K are invariant under isomorphism. Thus a symmetric matroid M induces on any finite graph G a uniquely determined matroid M(G). We study connectivity properties of circuits and generalized trees of symmetric matroids. We give several characterizations of a special class of symmetric matroids called connectivity matroids. These matroids play for generalized notions of higher vertex-connectivity for graphs a role similar to the role the polygon-matroid plays for simple connectivity. Our theorem generalizes earlier results by G. Kalai. Using our methods we also give a simple proof of a well-known theorem by Simoes-Pereira on matroidal families.", } @InProceedings{zpr91-103, author = "M. Middendorf and F. Pfeiffer", institution = mi, title = "The Paths-Selection-Problem", booktitle = "Proceedings of the 1st DIMACS Workshop on Polyhedral Combinatorics", location = "Morristown/NJ (USA)", year = "1990", series = "DIMACS, Ser. Discret. Math. Theor. Comput. Sci.", volume = "1", pages = "179--187", keywords = "grids, Euler paths, path selection problem, general paths-selection problem, NP-completeness; 05C38, 68R10", annote = "Let P and Q be two disjoint finite length paths with corresponding integer capacity functions c(sub P) and c(sub Q), and let S = {(s((sup P), (sub i)),s((sup Q), (sub i))): i in I} be a system of pairs of paths, the first a subpath of P and the second a subpath of Q. The path selection problem is ``Does there exists a choice-function h which respects the given capacities?'' (i.e., a function h: I -> {0,1} with |{i in h sup(-1)[0] : e in s((sup P), (sub i))}|<= c(sub P) (e) for e in E(P) and | {i in h sup(-1)[1] : e in s((sup Q), (sub i))}|<= c(sub Q) (e) for e in E(Q)). The general paths-selection problem is shown to be NP-complete. A special case of the problem is shown to be equivalent to finding the independence number of an interval graph. The complexity of other related problems, such as the ``multiterminal grid-joining problem'' and the ``Eulerian disjoint-paths problem'' are considered, and shown to be NP-complete as well.", } @Article{zpr91-102, author = "M. J{\"u}nger and A. Martin and G. Reinelt and R. Weismantel", institution = mi, title = "Quadratic 0/1 Optimization and a Decomposition Approach for the Placement of Electronic Circuits", journal = "Mathematical Programming", volume = "63", number = "3", pages = "257--279", year = "1994", keywords = "quadratic 0/1-optimization, VLSI-design, layout design of electronic circuits, NP-hardness, $\varepsilon$-approximative algorithms; 90C09, 90C20, 68Q35, 90C90", annote = "The placement problem in the layout design of electronic circuits consists of finding a non-overlapping assignment of rectangular cells to positions on the chip so that wireability is guaranteed and certain technical constraints are met. This problem can be modelled as a quadratic 0/1-program subject to linear constraints. We will present a decomposition approach to the placement problem and give results about NP-hardness and the existence of $\varepsilon$-approximative algorithms for the involved optimization problems.
A graphtheoretic formulation of these problems will enable us to develop approximative algorithms.
Finally we will present details of the implementation of our approach and compare it to industrial state of the art placement routines.", } @Article{zpr91-101, author = "M. Fellows and J. Kratochvil and M. Middendorf and F. Pfeiffer", institution = mi, title = "The Complexity of Induced Minors and Related Problems", journal = "Algorithmica", volume = "13", number = "3", pages = "266--282", publisher = "Springer-Verlag, New York, Inc.", year = "1995", crindex = "23k,7,zpr91-101.ps.gz", keywords = "graph minors, NP-completeness, treewidth; 68Q15, 68R10", annote = "The computational complexity of a number of problems concerning induced structures in graphs is studied, and compared with the complexity of corresponding problems concerning non-induced structures. The effect on these problems of restricting the input to planar graphs is also considered. The principal results include:
(1) Induced maximum matching and induced directed path are NP-complete for planar graphs,
(2) for every fixed graph H, induced H-minor testing can be accomplished for planar graphs O(n), and
(3) there are graphs H for which induced H- minor testing is NP-complete for unrestricted input.
Some useful structural theorems concerning induced minors are presented, including a bound on the treewidth of planar graphs that exclude a planar induced minor.", } @Article{zpr91-099, author = "T. Christof and M. J{\"u}nger and G. Reinelt", institution = inf, title = "A complete description of the travelling salesman polytope on 8 nodes", journal = "Operations Research Letters", volume = "10", number = "9", pages = "497--500", year = "1991", keywords = "polyhedral combinatorics, facets for the symmetric traveling salesman polytope; 90C27, 90C35, 52B12", annote = "We present three previously unknown classes of facets for the symmetric traveling salesman polytope STSP(8) on 8 nodes which we found using a computer code. These new inequalities now allow for the complete linear description of STSP(8).", } @InProceedings{zpr91-098a, author = "M. Middendorf and F. Pfeiffer", institution = mi, title = "On the complexity of the disjoint paths problem (Extended abstract)", booktitle = "Proceedings of the 1st DIMACS Workshop on Polyhedral Combinatorics", location = "Morristown/NJ (USA)", year = "1990", series = "DIMACS, Ser. Discret. Math. Theor. Comput. Sci.", volume = "1", pages = "171--178", keywords = "disjoint paths problem, disjoint circuits, edge-disjoint paths problem, vertex-disjoint paths problem, planar graphs; 05C38", } @Article{zpr91-098, author = "M. Middendorf and F. Pfeiffer", institution = mi, title = "On the Complexity of the Disjoint Path Problem", journal = "Combinatorica", volume = "13", number = "1", pages = "91--107", year = "1993", keywords = "NP-completeness, planar edge-disjoint paths, vertex disjoint paths, half-integral relaxation; 68Q25, 68R10, 05C38, 05C45, 05C10", annote = "We consider the disjoint paths problem. Given a graph G and a subset S of the edge-set of G the problem is to decide whether there exists a family F of disjoint circuits in G each containing exactly one edge of S such that every edge in S belongs to a circuit in C. By a well-known theorem of P. Seymour [On odd cuts and plane multicommodity flows, Proc. London Math. Soc.(3) 42, 178-192 (1981)] the edge-disjoint paths problem is polynomially solvable for Eulerian planar graphs G.
We show that (assuming $P \ne NP$) one can drop neither planarity nor the Eulerian condition on G without losing polynomial time solvability. We prove the NP-completeness of the planar edge-disjoint paths problem by showing the NP-completeness of the vertex disjoint paths problem for planar graphs with maximum vertex-degree three. This disproves (assuming $P \ne NP$) a conjecture of A. Schrijver [Homotopic Routing Methods, in: Paths, Flows and VLSI Layout, Algorithms Comb. 9, 329-371 (1990)] concerning the existence of a polynomial time algorithm for the planar vertex-disjoint paths problem. Furthermore we present a counterexample to a conjugate of A. Frank mentioned in A. Seboe [Dual Integrality and Multicommodity Flows. Combinatorics, Colloquia Mathematica Societatis Janos Bolyai, 52, 453-469 (1988)]. This conjecture would have implied a polynomial algorithm for the planar edge-disjoint paths problem. Moreover we derive a complete characterization of all minor-closed classes of graphs for which the disjoint paths problem is polynomially solvable. Finally we show the NP-completeness of the half-integral relaxation of the edge-disjoint paths problem. This implies an answer to the long-standing question whether the edge-disjoint paths problem is polynomially solvable for Eulerian graphs.", } @TechReport{zpr91-097, author = "A. Bachem and M. Wottawa", institution = mi, title = "Ein 18512-St{\"a}dte (Deutschland-)Traveling-Salesman-Problem", year = "1991", keywords = "traveling salesman problem; 90B05, 90C27", } @Article{zpr90-096, author = "M. J{\"u}nger and G. Reinelt and D. Zepf", institution = mi, title = "Computing Correct Delaunay Triangulations", journal = "Computing", volume = "47", number = "1", pages = "43--49", year = "1991", keywords = "Delaunay triangulation, Voronoj diagram, geometric optimization algorithms, numerically stable computer implementation, computational geometry; 65Y25, 68U05, 32B25", annote = "In recent years the practical computation of Delaunay triangulations resp. Voronoi diagrams has received a lot of attention in the literature. While the Delaunay triangulation is an important basic tool in geometric optimization algorithms, it is nontrivial to achieve a numerically stable computer implementation. In this technical note we assume that all generating points are grid points of a regular M by M lattice in the plane. Depending on M we derive the necessary word length a binary computer must have for integer representation in order to obtain exact Delaunay triangulations. This analysis is carried out for the L1-, L2- and L-infinity-metric.", } @Article{zpr90-095, author = "W. Hochst{\"a}ttler", institution = mi, title = "A Lattice-Theoretical Characterization of Oriented Matroids", journal = "European Journal of Combinatorics", publisher = "Academic Press", volume = "18", number = "5", pages = "563--574", month = jul, year = "1997", crindex = "75k,15,zpr90-095.ps.gz", keywords = "Oriented Matroids, Matroids, Face Lattice, Combinatorial Pseudomanifold, Topology, Geometry; 05B35, 06B30, 51D20, 52B40", annote = "If $\Pscr$ is the big face lattice of the cocircuits of an oriented matroid, it is well known that the zero-map is a cover-preserving, order-reversing surjection onto the geometric lattice of the underlying (unoriented) matroid. In this paper we give a (necessary and) sufficient condition for such maps to come from the face lattice of an oriented matroid.", } @InCollection{zpr90-094, author = "M. J{\"u}nger and K. H. Borgwardt and N. Gaffke and G. Reinelt", booktitle = "Applied Geometry and Discrete Mathematics", note = "The Victor Klee Festschrift", editor = "P. Gritzmann and B. Sturmfels", institution = mi, series = "DIMACS Series in Discrete Mathematics and Theoretical Computer Science", title = "Computing the convex hull in the Euclidean plane in linear expected time", volume = "4", pages = "91--108", year = "1991", keywords = "expected runtime, convex hull algorithms; 68U05, 60D05", annote = "There are many algorithms for computing the convex hull of a set of n points in the Euclidean plane in worst case time O(n*ln(n)). It is also known that O(n) average time behavior can be achieved under the assumption that the n points are independently and uniformly distributed over the unit square or the unit disk. We will show how any O(n*ln(n)) worst case time algorithm for the convex hull can be converted into an O(n) average time algorithm under this assumption. Also, it turns out that O(n) average time is still obtained if algorithms of higher worst case time complexity are used. Finally, we will give a computational comparison of our method with other linear expected time algorithms for problems instances in the unit square.", } @Article{zpr90-093, author = "H.-J. Rieder", institution = mi, title = "A Note on the f-Factor Lattice of Bipartite Graphs", journal = "Journal of Combinatorial Theory B", volume = "56", number = "1", pages = "90--96", year = "1992", keywords = "f-factor, bipartite graphs, perfect matchings, matroids; 05C70, 05C75, 05B35", } @PhdThesis{zpr90-092, author = "U. R{\"u}tsch", school = mi, title = "Charakterisierung ganzzahliger Gitter {\"u}ber kombinatorischen Strukturen", year = "1990", keywords = "integral lattices; combinatorial structures; matching; bases of matroides; aborescence; 05C70, 05B35", annote = "Im ersten Kapitel werden die st{\"a}ndig ben{\"o}tigten Begriffe und Notationen kurz definiert und ihre wesentlichen Eigenschaften angesprochen. F{\"u}r die vorliegende Arbeit haben wir uns auf graphentheoretische sowie matroidtheoretische Grundlagen beschr{\"a}nkt. Auf eine Darstellung der Komplexit{\"a}tstheorie ist hier verzichtet worden, da die komplexit{\"a}tstheoretischen Untersuchungen nicht Hauptanliegen dieser Art sind. Bei Problemklassifikationen weren wir stets ``leichte'' bzw. ``schwere'' Probleme im Sinne von polynomial l{\"o}sbar bzw. NP-vollst{\"a}ndig unterscheiden. Genaue Definitionen findet man in M. R. Garey and D. S. Johnson [Computers and interactability. A guide to the theory of NP-completeness (1979)].
Im zweiten Kapitel wird der Zusammenhang der Existenz perfekter Matchings in bipartiten Graphen und der Existenz gerichteter, knotendisjunkter Wege in gerichteten Graphen untersucht. Schon bei der algorithmischen L{\"o}sung des Optimierungsproblems in bipartiten Graphen, bei vorgegebener Kantengewichtung ein perfektes Matching mit minimaler Kantenbewertung zu bestimmen, wird die Idee alternierender Wege im ungerichteten Graphen durch gerichtete Wege in einem speziellen gerichteten Graphen verwirklicht, indem man jeweils eine Nicht-Matchingkante durch eine Matchingkante verl{\"a}ngert. Diese Idee kann auch bei der Untersuchung des lokalen Zusammenhangproblems in gerichteten Graphen verwendet werden. Die Untersuchungen f{\"u}hren zu einem speziellen Matchingproblem, welches dargestellt und in Spezialf{\"a}llen gel{\"o}st werden kann.
Die folgenden beiden Kapitel behandeln die Gitterdarstellung kombinatorischer Probleme. Die allgemein verwendeten Begriffe und Ergebnisse, insbesondere die Darstellung des dualen Moduls und dessen Verwendung zur Darstellung der gesuchten Gittercharakterisierung werden im ersten Abschnitt des dritten Kapitels genannt. Im n{\"a}chsten Abschnitt dieses Kapitels wird kurz das Ergebnis f{\"u}r Gitter von Matroidbasen dargestellt, das in seiner speziellen Form f{\"u}r graphische Matroide im vierten Kapitel ben{\"o}tigt wird. Es folgen die ausf{\"u}hrliche Darstellung und Beweisskizze der Gittercharakterisierung des Matching-Gitters im bipartiten bzw. allgemeinen Fall. Hier werden die Ergebnisse von L. Lovász [Theory of algorithms, Colloq. Pecs/Hung. 1984, Colloq. Math. Soc. Janos Bolyai 44, 323-337 (1986)], [J. Comb. Theory, Ser. B 43, 187-222 (1987)] in einer Form wiedergegeben, die die Analogien in der Beweistechnik bei der Charakterisierung von Gittern {\"u}ber kombinatorische Strukturen klar erkennen l{\"a}{\"s}t. Wesentliche Schritte sind hier:

  • Dekomposition des Graphen in Teilgraphen mit st{\"a}rkeren Eigenschaften, im Matchingfall in Teilgraphen ohne nicht-trivale strikte Schnitte;
  • Darstellung der Teilgitter, dabei wird in der Regel das Duale des Gitters untersucht;
  • {\"U}bertragung der Ergebnisse auf den gesamten Graphen.
    Als Hauptergebnis der vorliegenden Arbeit wird im vierten Kapitel die Charakterisierung des Gitters von Arboreszenzen in gerichteten Graphen hergeleitet. Dabei kann die im vorhergehenden Kapitel entwickelte Beweismethode verwendet werden. Dazu wird der Graph zun{\"a}chst in seine stark-zusammenh{\"a}ngenden Komponenten zerlegt. Es folgt die Charakterisierung der Arboreszenzen-Gitter stark zusammenh{\"a}ngener Graphen. Die Darstellung des Dualen erm{\"o}glicht dann die Charakterisierung des Gitters f{\"u}r Graphen, deren Arboreszenzen stets die gleiche Wurzel haben. Im letzten Schritt werden diese beiden Ergebnisse zur Charakterisierung des Arboreszenzen-Gitters verwendet.", } @Article{zpr90-091, author = "M. Middendorf and F. Pfeiffer", institution = mi, title = "Weakly Transitive Orientations, Hasse Diagrams and String Graphs", journal = "Discrete Mathematics", volume = "111", number = "1-3", pages = "393--400", year = "1993", keywords = "weakly transitive orientation, characterization, Hasse diagrams, weakly transitive orientable graphs, intersection graphs, planar graphs, circular-permutation graphs, circular-arc graphs, comparability graphs, permutation graphs, interval graphs, recognition problem, string graphs, NP-completeness, NP-hardness, complexity; 05C75, 68R10, 05C99", annote = "We introduce the notion of a weakly transitive orientation for graphs as a natural generalization of transitive orientations and give a characterization for weakly transitive orientations in terms of forbidden substructures. As a corollary of this characterization, we get that the Hasse diagrams of posets are exactly the triangle-free weakly transitive oriented graphs. Moreover, we characterize the complements of weakly transitive orientable graphs as a special class of intersection graphs of paths in planar graphs. In this way, complements of weakly transitive orientable graphs prove to form a common generalization of several known classes of intersection graphs such as circular-permutation graphs (and, thus, circular-arc graphs), complements of comparability graphs (and, thus, permutation graphs and interval graphs). An immediate consequence of this theorem is an intersection graph characterization of Hasse diagrams. Using this characterization, we obtain a simple reduction of the problem to decide for a graph whether it admits an orientation as a Hasse diagram to the recognition problem for string graphs. Using a result of Nesetril and Roedl that Hasse diagram orientation is NP-complete, this gives a new proof for NP-hardness of the string graph recognition problem. The status of complexity of the recognition problem for string graphs (intersection graphs of curves in the plane) was a long-standing open problem until J. Kratochvil gave a (rather involved) NP-hardness proof in 1988, see [J. Comb. Theory, Ser. B 52, No. 1, 67-78 (1991)].", } @Article{zpr90-090, author = "A. W. M. Dress and W. Hochst{\"a}ttler and W. Kern", institution = mi, title = "Modular Substructures in Pseudomodular Lattices", journal = "Math. Scand.", volume = "74", number = "1", pages = "9--16", year = "1994", keywords = "geometric lattices, modular sublattices, pseudomodular lattices; 06C10, 05B35", annote = "Pseudomodular lattices have been used by the first author and L. Lovász [Combinatorica 7, 39-48 (1987)] in order to investigate combinatorial properties of algebraic matroids and were further analyzed by A. Bj{\"o}rner and L. Lovász [Acta Sci. Math. 51, No. 3/4, 295-308 (1987)]. The purpose of our paper is to present local conditions, characterizing modular sublattices of a pseudomodular lattice. As an application, we derive a result by the second and the third author [Combinatorica 9, No. 2, 145-152 (1989)], implying that Lovász's min-max formula for matchings in projective geometries remains valid for pseudomodular lattices, and we discuss a relation with B. Lindstroems construction of subgeometries of full algebraic combinatorial geometries which are isomorphic to projective geometries over skew fields.", } @TechReport{zpr90-089, author = "U.-D. Radicke", institution = inf, title = "The Complexity of Multi-Spindle Drilling Problems", year = "1990", } @Article{zpr90-088, author = "M. Hofmeister", institution = mi, title = "Non-Equivalent Cocycles of Graphs over Finite Fields", journal = "Ars Combinatoria", volume = "36", pages = "119--127", year = "1993", keywords = "automorphism group, cocycle space, orbits, finite fields, enumeration, edge cuts; 05C25, 05C38", annote = "The automorphism group of a graph acts on its cocycle space over any field. The orbits of this group action will be counted in case of finite fields. In particular, we obtain an enumeration of non-equivalent edge cuts of the graph.", } @Article{zpr90-087, author = "R. Ewen and M. Hofmeister", institution = mi, title = "On Coverings of the Complete Graph with 4 Vertices", journal = "Ars Combinatoria", volume = "35", pages = "87--96", year = "1993", keywords = "enumeration, covering graph, complete graph, permutation group; 05C30, 05C25", annote = "It is shown that isomorphism classes of r-fold covering spaces over the complete graph K4 can be represented by orbits of a certain permutation group. Two structure theorems concerning this group are presented. (Summary)", } @Article{zpr90-086, author = "U. Faigle and W. Kern", institution = mi, title = "Some Order Dimension Bounds for Communication Complexity Problems", journal = "Acta Informatica", volume = "28", number = "6", pages = "593--601", year = "1991", keywords = "ordered sets, communication complexity; 68Q25, 68R99", annote = "We associate with a general (0,1)-matrix M an ordered set P(M) and derive lower and upper bounds for the deterministic communication complexity of M in terms of the order dimension of P(M). We furthermore consider the special class of communication matrices M obtained as cliques vs. stable sets incidence matrices of comparability graphs G. We bound their complexity by O((log d)$\cdot (\log n))$, where n is the number of nodes of G and d is the order dimension of an orientation of G. In this special case, our bound is shown to improve other well-known bounds obtained for the general cliques vs. stable set problem.", } @TechReport{zpr90-085, author = "S. Baas and W. Kern and W. M. Nawijn", institution = mi, title = "Scheduling Jobs on Parallel Machines, each with a Unit-Capacity Buffer", keywords = "scheduling, delay-loss system, unit-capacity buffers, dynamic programming; 05A15, 90B35", annote = "Given are a set of k parallel machines and a set of n jobs which arrive at fixed times. Each job has a fixed, but machine-dependend processing time and value. Each machine can process one job at a time. A job is processed either immediately after its time of arrival or after having spent some time in a buffer, or it is rejected. It is shown that under certain weak conditions the problem of finding a minimum weight schedule can be solved in polynomial time, but that it becomes NP-complete if such conditions do not hold.", } @Article{zpr90-084, author = "W. Hochst{\"a}ttler and H.-J. Rieder", institution = mi, title = "A Note on the Lattice of 2-Matroid-Intersections", journal = "Archiv der Mathematik", publisher = "Birkhäuser", volume = "57", number = "5", pages = "514--517", year = "1991", keywords = "point lattice, matroid-intersection; 05B35", annote = "By considering a matroid generalization of the graphic matroid on the K4 it is shown that in general the lattice generated by the common bases of a matroid M and a partition matroid Q (which satisfy a rank-condition) is not the intersection of the two lattices associated with the bases of M and Q, respectively. (Which is true for the intersection of two partition-matroids and that of an arbitrary matroid with a bipartition matroid.)", } @Article{zpr90-083, author = "U. Faigle and W. Kern", institution = mi, title = "Some Convergence Results for Probabilistic Tabu Search", journal = "ORSA Journal on Computing", volume = "4", number = "1", pages = "32--37", year = "1992", keywords = "local search, tabu search, memory based strategies, simulated annealing; 90C27, 90-08", annote = "During recent years, much work has gone into the exploration of general fundamental principles underlying local search strategies for combinatorial optimization. Many of these strategies can be subsumed under the general framework of tabu search, which introduces mechanisms of guidance and control based on flexible memory processes, broadening the range of strategic possibilities beyond those incorporated in memoryless search heuristics such as simulated annealing. We consider some examples of such memory based strategies for modifying both the generation and acceptance probabilities and investigate their impact on convergence results. It turns out that several tabu search ideas can be subjected to mathematical analysis similar to those applied to simulated annealing, making it possible to establish corresponding convergence properties based on a broader foundation.", } @TechReport{zpr90-082, author = "W. M. Nawijn and W. Kern and S. Baas", institution = mi, title = "Minimum Loss Scheduling", year = "1990", keywords = "scheduling, delay-loss system, complexity, dynamic programming; 05A15, 90B35", annote = "Consider a single machine with buffer of capacity one for waiting jobs. Given the arrival epochs, the weights and the processing times of n consecutive future jobs, a maximum weight subset of jobs is to be found that is schedulable without violating the buffer's capacity constraint. A polynomial algorithm for the unweighted loss-delay problem is presented. For the weighted one-machine case, shown to be NP-hard, a dynamic programming formulation is given.", } @TechReport{zpr90-081, author = "W. Hochst{\"a}ttler", institution = mi, title = "Vertex-Edge-Paths and a Forbidden Facet", year = "1990", } @InProceedings{zpr89-080, author = "W. Hochst{\"a}ttler", institution = mi, title = "Shellability of Oriented Matroids", booktitle = "Proceddings of the IPCO '90", editors = "R. Karman and W. R. Pulleyblank", pages = "275--282", year = "1990", publisher = "University of Waterloo Press", crindex = "41k,10,zpr89-80.ps.gz", annote = "A. Mandel proved that the maximal cells of an Oriented Matroid poset are B-shellable. Our result shows that the whole Oriented Matroid is shellable, too.", } @PhdThesis{zpr89-079, author = "H.-J. Rieder", school = mi, title = "Gitterstrukturen bei Matroidproblemen", year = "1989", crindex = "155k,65,zpr89-79.ps.gz", keywords = "lattice structures, matroid problems; 05B35", annote = "In der vorliegenden Arbeit untersuchen wir Gitter, die von Matroidstrukturen und 2-Matroidschnitten, zwei Grundstrukturen zahlreicher Optimierungsprobleme, erzeugt werden.
    Im ersten Kapitel stellen wir die notwendigen Grundlagen {\"u}ber Gitter, Graphen und Matroide zur Verf{\"u}gung.
    Anschlie{\"s}end charakterisieren wir im zweiten Kapitel die Gitter der Matroidbasen, wobei wir lediglich die Matroidaxiome ben{\"o}tigen. Daneben zeigen wir die Dualit{\"a}t der von den Kreisen graphischer und cographischer Matroide generierten Gitter und geben einige Beispiele f{\"u}r weitere Kreisgitter von Matroiden.
    Im dritten Kapitel besch{\"a}ftigen wir uns dann mit dem Schnitt zweier Matroide M und N. Wir diskutieren eine Rangbedingung, die einerseits garantiert, da{\"s} M und N gemeinsame Basen besitzen, und die andererseits eine Dekomposition des betrachteten Problems verhindert. Die direkte Verallgemeinerung des von Lovász untersuchten bipartiten Matchings auf den Schnitt zweier Partitionsmatroide (bzw. das hierzu {\"a}quivalente Problem der f-Faktoren in bipartiten Graphen) erlaubt eine sch{\"o}ne Beschreibung des zugeh{\"o}rigen Gitters. Hier ist das von den gemeinsamen Basen von M und N aufgespannte Gitter genau der Schnitt der beiden Gitter der Basen von M bzw. N, eine im allgemeinen f{\"u}r Gitter ungew{\"o}hnliche Eigenschaft. Dieses Ergebnis bleibt auch dann g{\"u}ltig, wenn M ein beliebiges Matroid ist, falls N nur zwei Komponenten besitzt. Erst ab drei Partitionsklassen bei N wird das von den gemeinsamen Basen von M und N erzeugte Gitter, wie auch im allgemeinen Fall, zus{\"a}tzlich von Eigenschaften des Schnittproblems bestimmt, die nicht auf ein Matroid alleine zur{\"u}ckzuf{\"u}hren sind. Ein Beispiel hierf{\"u}r ist der starke Zusammenhang von gerichteten Graphen beim Schnitt des graphischen mit dem Endpunktpartitions-Matroid.
    Im abschlie{\"s}enden Kapitel geben wir eine kommentierende Kurzzusammenfassung der Ergebnisse und stellen noch einige weiterf{\"u}hrende Probleme vor.", } @Article{zpr89-078, author = "B. Fa{\ss}bender", institution = mi, title = "A Sufficient Condition on Degree Sums of Independent Triples for Hamiltonian Cycles in 1-Tough Graphs", journal = "Ars Combinatoria", volume = "33", pages = "300--304", year = "1992", keywords = "Hamiltonian cycles, 1-tough graph; 05C45", } @TechReport{zpr89-077, author = "W. Kern", institution = mi, title = "Informatik - Vorlesungsmanuskript", year = "1989", } @TechReport{zpr89-076, author = "A. Bachem", institution = mi, title = "Komplexit{\"a}tstheorie - Vorlesungsmanuskript", year = "1989", } @TechReport{zpr89-075, author = "A. Bachem and R. Kannan", institution = mi, title = "Linear Algebra: {A} Computational Complexity Approach", year = "1989", } @Book{zpr89-074, author = "A. Bachem and W. Kern", institution = mi, title = "Linear Programming Duality. An Introduction to Oriented Matroids", series = "Universitext", publisher = "Springer-Verlag", pages = "216", year = "1992", keywords = "oriented matroids, duality, polyhedra, Farkas lemma, partially ordered sets; 90C05, 90C27, 05B35, 52B12", annote = "This book presents an elementary introduction to the theory of oriented matroids. The way oriented matroids are introduced emphasizes that they are the most general - and hence simplest - structures for which linear Programming Duality results can be stated and proved. The main theme of the book is duality. Using Farkas' Lemma as the basis the authors start with results on polyhedra in Rn and show how to restate the essence of the proofs in terms of sign patterns of oriented matroids. Most of the standard material in Linear Programming is presented in the setting of real space as well as in the more abstract theory of oriented matroids. This approach clarifies the theory behind Linear Programming and proofs become simpler. The last part of the book deals with the facial structure of polytopes respectively their oriented matroid counterparts. It is an introduction to more advanced topics in oriented matroid theory. Each chapter contains suggestions for further reading and the references provide an overview of the research in this field.", } @Article{zpr89-073, author = "A. Bachem and A. W. M. Dress and W. Wenzel", institution = mi, title = "Five Variations on a Theme by Gyula Farkas", journal = "Advances in Applied Mathematics", volume = "13", number = "2", pages = "160--185", month = jun, year = "1992", keywords = "Farkas lemma, matroid theory; 51D20, 05B35, 51M05", } @TechReport{zpr89-072, author = "Arbeitsgruppe Optimierung", institution = mi, title = "Jahresbericht 1988", year = "1989", } @Misc{zpr89-071, author = "W. Kern", institution = mi, title = "Verfahren der kombinatorischen Optimierung und ihre {G}{\"u}ltigkeitsbereiche", year = "1989", } @TechReport{zpr89-070, author = "U. Faigle and W. Kern", institution = mi, title = "A Note on the Communication Complexity of Totally Unimodular Matrices", year = "1989", } @TechReport{zpr89-069, author = "A. Bachem and K. Harf and I. Kellershohn", institution = mi, title = "Zur Problematik eines Schichtenmodells bei der optimalen Bestandsanpassung von Bausparkollektiven", year = "1989", } @TechReport{zpr89-068, author = "A. Bachem and M. Niezborala", institution = mi, title = "Numerische Erfahrungen bei der Vektorisierung linearer Programmierungsalgorithmen", year = "1989", } @Article{zpr89-067, author = "U. Faigle and W. Kern", institution = mi, title = "Note on the Convergence of Simulated Annealing Algorithms", journal = "SIAM Journal on Control and Optimization", volume = "29", number = "1", pages = "153--159", year = "1991", keywords = "inductive proof, stationary distributions of a simulated annealing algorithm, weak reversibility condition; 90C27, 90-08", annote = "Generalizing the results of the first author and R. Schrader [Inf. Process. Lett. 27, 189-194 (1988)] a short inductive proof is given that shows that the stationary distributions of a simulated annealing algorithm converge to a distribution where nonoptimal elements are generated with probability zero, provided that the ``weak reversibility condition'' of B. Hajek [Math. Oper. Res. 13, No. 2, 311-329 (1988)] holds.", } @Article{zpr89-066, author = "U. Faigle and W. Kern and G. Turán", institution = mi, title = "On the Performance of On-Line Algorithms for Partition Problems", journal = "Acta Cybernetica", volume = "9", number = "2", pages = "107--119", year = "1989", keywords = "partition problems, combinatorial optimization, matroid, graph partitioning; 68Q25, 90C27, 05B35, 05C35, 68R10", annote = "We consider the performance of the greedy algorithm and of on-line algorithms for partition problems in combinatorial optimization. After surveying known resuls we give bounds for matroid and graph partitioning, and discuss the power of non-adaptive adversaries for proving lower bounds.", } @TechReport{zpr89-065, author = "A. Bachem and A. Reinhold", institution = mi, title = "On the Complexity of the Farkas-Property of Oriented Matroids", crindex = "53k,12,zpr89-65.ps.gz", keywords = "oriented matroids;", annote = "We extend results of Hausmann and Korte (1981) to oriented matroids showing how Basis-, Circuit-, Span-, Flat-, Minty- and Farkas-oracle computationally relate to each other.", } @Article{zpr89-064, author = "A. Bachem and W. Kern", institution = mi, title = "A Guided Tour through Oriented Matroid Axioms", journal = "Acta Mathematicae Applicatae Sinica", volume = "9", number = "2", pages = "125--134", year = "1993", keywords = "axiom systems, oriented matroids, Farkas' Lemma; 05B35, 52B40", annote = "Oriented Matroids arise as a natural combinatorial abstraction of linear algebra and geometry. Some of the topics were foreseen by Rockafellar. Later, oriented matroids were independently discovered by Bland, Dress and Las Vergnas. As with matroids oriented matroids can be developed from many different axiom systems. In this survey we shall concentrate on some of the more important ones and show how one system can be deduced from the other.
    Moreover we show how these axiom systems computationally relate each qother proving that none of them can be used to check one side of the well known Farkas' Lemma.", } @Article{zpr89-062, author = "M. Hofmeister", institution = mi, title = "Concrete Graph Covering Projections", journal = "Ars Combinatoria", volume = "32", pages = "121--127", year = "1991", keywords = "graph covering projections, graph homomorphism, permutation voltage assignment, r-fold covering projection; 05C30, 05C25", annote = "A graph covering projection is a local graph homeomorphism. Certain partitions of the vertex set of the preimage graph induce a notion of ``concreteness''. The concrete graph covering projections will be counted up to isomorphism.", } @TechReport{zpr88-063, author = "Arbeitsgruppe Optimierung", institution = mi, title = "Jahresbericht 1986/87", year = "1988", } @Article{zpr88-061, author = "M. Leclerc and F. Rendl", institution = mi, title = "k-best Constrained Bases of a Matroid", journal = zor, volume = "34", number = "2", pages = "79--89", year = "1990", keywords = "ranking, k-best bases, matroids; 90C27, 05B35", annote = "We propose a method for finding a set of k-best bases of an arbitrary matroid where the bases are required to satisfy additional partitionlike constraints. An application of this problem is discussed.", } @InProceedings{zpr88-060, author = "A. Wanka", institution = mi, title = "Interior and Exterior Methods of Linear Programming", booktitle = "Operations Research Proceedings 1988", editor = "D. Pressmar and K. E. J{\"a}ger and H. Krallmann and H. Schellhaas and L. Streitfeldt", pages = "214--221", year = "1989", publisher = "Springer-Verlag", } @InCollection{zpr88-059, author = "A. Wanka", institution = mi, title = "On First Experiences with the Implementation of a Newton Based Linear Programming Approach", booktitle = "Séminaire Lotharingien de Combinatoire (Oberfranken, 1990)", pages = "127--140", publisher = "Univ. Louis Pasteur", address = "Strasbourg", year = "1990", keywords = "Cholesky-factorization, combinatorial matrix, exterior point linear programming, linear equation system, Newton's method, rank-one updates", annote = "This paper presents the implementation of an exterior point linear programming approach introduced by Betke. In every iteration of this algorithm Newton's method is used in order to determine nearest points of two convex sets. The method is simple to implement, fully exploits sparsity and at the presence of rounding errors it achieves high precision and stability.
    Beside the nice geometric proceeding a particular interest in this method is derived from the following observation: In Karmarkar's as well as in this algorithm one has to solve a linear equation system of the form AD2ATy=b. The solution of this system is the most time consuming part in linear programs. While in Karmarkar's method the entries of the diagonal Matrix D are the coordinates of the iteration point, the diagonal entries are either 0 or 1 in our method. Hence throughout this paper D is a purely combinatorial matrix which yields to reasonable numbers of rank one updates of the corresponding Cholesky factor of AD2AT. Moreover, the Cholesky factors become sparser than in Karmarkar's approach.", } @TechReport{zpr88-058, author = "H.-J. Rieder", institution = mi, title = "The Lattice of the Intersection of two Partition Matroids", year = "1988", keywords = "incidence vectors, lattice of intersection, partition matroids;", annote = "We determine the lattice in R|E| generated by the incidence vectors corresponding to the bases of the intersection of two partition matroids P and Q on the same finite set E.
    We give a basis of the lattice and show that - if a rank condition is satisfied - the lattice of the intersection is the same as the intersection of the two lattices generated by the incidence vectors of the bases of P and Q, respectively.", } @Article{zpr88-057, author = "B. Fa{\ss}bender", institution = mi, title = "On Longest Cycles and Strongly Linking Vertex Sets", journal = "Journal of Graph Theory", volume = "13", number = "6", pages = "697--702", year = "1989", keywords = "non-hamiltonian graph, longest cycle; 05C38", annote = "Let G be a simple non-hamiltonian graph, let C be a longest cycle in G, and let p be a positive integer. By considering a special form of connectivity, we obtain a sufficient condition on degrees for the non-existence of (p-1)-path-connected components in G-C.", } @Article{zpr88-056, author = "M. Hofmeister", institution = mi, title = "Isomorphisms and Automorphisms of Graph Coverings", journal = "Discrete Mathematics", volume = "98", number = "3", pages = "175--183", year = "1991", keywords = "r-fold covering of a graph, automorphism group, covering projections, permutation voltage assignment, lifting automorphism, labeled graphs; 05C70, 05C10, 05C78", annote = "Any group of automorphisms of a graph G induces a notion of isomorphism between covering projections of G. We consider liftings of automorphisms of G and classify the isomorphism classes of covering projections of G by means of permutation voltage assignments.", } @Article{zpr88-055, author = "M. Leclerc and F. Rendl", institution = mi, title = "Constrained Spanning Trees and the Travelling Salesman Problem", journal = "European Journal of Operational Research", volume = "39", number = "1", pages = "96--102", year = "1989", keywords = "lower bound, 1-trees, degree-constraints, subgradient optimization; 90C35, 65K05, 05C05", annote = "Minimum weight 1-trees provide a well-known lower bound for the symmetric traveling salesman problem. We propose to strengthen this bound by imposing degree-constraints upon the 1-trees. The vertices for the constraints are chosen to form a stable set S. We propose an O(m loglog n +|S|(n|S|+m \alpha(m,n))) algorithm for this problem and report on its use in a Lagrangian approach to the traveling salesman problem.", } @Article{zpr88-054, author = "D. Jungnickel and M. Leclerc", institution = mi, title = "A Class of Lattices", journal = "Ars Combinatoria", volume = "26", pages = "243--248", year = "1988", keywords = "lattice, trivial Steiner system, k-uniform matroids; 05B35", annote = "We determine the lattice in Zn generated by those vectors having exactly k components 1 and the remaining n-k components 0; we also exhibit a ``nice'' basis for this lattice. Note that the generating vectors are in a natural way associated with well-known combinatorial objects. They are the characteristic vectors of both the blocks of the trivial Steiner system S(k,k,n) and the bases of the k-uniform matroid on n points. We also obtain the corresponding polyhedron and point out an interesting sublattice (in the case n=m² arising from Combinatorial Matrix Theory.", } @TechReport{zpr88-053, author = "M. Leclerc", institution = mi, title = "Fast Polynomial Arithmetic and Exact Matchings", year = "1988", keywords = "complexity, matchings, pseudo-polynomial, knapsack equation; 90B05", annote = "Given a graph, a function w from E to Z+, and an integer b. A pseudo-polynomial algorithm is presented, which determines a perfect matching M of G such that the sum of w(e) over e in M equals b.", } @Article{zpr88-052, author = "M. Leclerc", institution = mi, title = "A Linear Algorithm for Breaking Periodic Vernam Ciphers", journal = "Ars Combinatoria", volume = "26", pages = "243--248", year = "1988", keywords = "data security; 94A60", } @InCollection{zpr88-051, author = "A. Bachem and B. Korte and R. Schrader", institution = mi, title = "Mathematische Modelle f{\"u}r Bausparkollektive", booktitle = "Bankpolitik - finanzielle Unternehmensf{\"u}hrung und die Theorie der Finanzm{\"a}rkte", editor = "B. Rudolf and J. Wilhelm", publisher = "Duncker \& Humblot, Berlin", year = "1988", } @Article{zpr88-050, author = "H.-J. Rieder", institution = mi, title = "The Lattices of Matroid Bases and Exact Matroid Bases", journal = "Archiv der Mathematik", publisher = "Birkhäuser", volume = "56", number = "6", pages = "616--623", year = "1991", keywords = "matroid bases; 05B35", annote = "Let M be a matroid on E and R be a subset of E. We show that the lattice generated by the incidence vectors of the bases of M is always that of a partition matroid. If we consider only bases B satisfying $\vert B \cap R \vert =p$, it is proved that the corresponding lattice is the intersection of the basis lattice of M with the hyperplane arising from the condition $\vert R \cap B \vert =p$.", } @Article{zpr88-049, author = "M. Alfter and W. Kern and A. Wanka", institution = mi, title = "On Adjoints and Dual Matroids", journal = "Journal of Combinatorial Theory B", volume = "50", number = "2", pages = "208--213", year = "1990", keywords = "dual matroid; 05B35", annote = "Duality among matroids is a well-known and well-understood relation. Besides this ``set-theoretical'' version of duality, there is another one based on lattice-theoretical concepts, which has been introduced by A. Cheung [Adjoints of a geometry, Canadian Math. Bul. 17, 363-365 (1974)]. These two concepts do not seem to fit into one another very well and their relationship (provided there is any) is more than unclear. In general, matroids may fail to have ``duals'' in the lattice-theoretical sense. Therefore, a natural question, posed by J.H. Mason [Glueing matroids together: a study of Dilworth truncations and matroid analogues of exterior and symmetric powers, in: Algebraic Methods in graph theory, L. Lovász and V.T. Sós, eds., North-Holland, Amsterdam (1981), is the following: If M does have a dual in the lattice theoretical sense, does M* (the set-theoretical dual of M) also have one? We present a counterexample, showing that the answer is negative.", } @TechReport{zpr87-048, author = "U. R{\"u}tsch", institution = mi, title = "The Arborescence Lattice", year = "1987", annote = "Let G = (V,E) be a directed graph and A the set of incidence vectors of arborescences of G. A wellknown approach in combinatorial optimization uses the characterization of the convex hull spanned by these vectors. In this paper, we describe the lattice generated by A.", } @PhdThesis{zpr87-047, author = "M. Leclerc", school = mi, title = "Algorithmen f{\"u}r kombinatorische Optimierungsprobleme mit Partitionsbeschr{\"a}nkungen", pages = "90", year = "1987", keywords = "matroid optimization, matching, partition constraints, exact constraints, budged constraints, degree restricted trees, travelling salesman, Pfaffian graphs; 90C10, 68Q25, 90C27, 05B35, 65K05, 05C70, 90-02", } @Article{zpr87-046, author = "B. Fa{\ss}bender", institution = mi, title = "Kriterien vom Ore-Typ f{\"u}r l{\"a}ngste Kreise in 2-zusammenh{\"a}ngenden Graphen", journal = "Mathematische Nachrichten", volume = "142", pages = "287--296", year = "1989", keywords = "dominating cycle; 2-connected graph; Hamiltonian graph; longest cycle; 05C38, 05C35, 05C45", annote = "Let G be a simple 2-connected graph of order $\nu$ such that the degree-sum of any two nonadjacent vertices is at least ${2 \over 3} \nu$, and let C be a non-dominating longest cycle in G. We show that G-C is a complete graph and V(G) contains a nonempty proper subset S such that G-S has exactly |S|+1 components. From this result a sufficient condition for the existence of Hamilton cycles in 1-tough graphs can be obtained.", } @Article{zpr87-045, author = "W. Hochst{\"a}ttler and W. Kern", institution = mi, title = "Matroid Matching in Pseudomodular Lattices", journal = "Combinatorica", volume = "9", number = "2", pages = "145--152", year = "1989", keywords = "matroid matching, minimax formula, pseudomodular matroids; 05B35", annote = "The matroid matching problem (also known as matroid parity problem) has been intensively studied by several authors. Starting from very special problems, in particular the matcing problem and the matroid intersection problem, good characterizations have been obtained for more and more general classes of matroids. The two most recent ones are the class of represetable matroids and, later on, the class of algebraic matroids, cf. L. Lovász [Selecting independent lines from a family of lines in projective space, Acta Sci. Math. 42, 121-131 (1980)] when M is a projective space. Later on, the minimax form and A.W.M. Dress and L. Lovász [On some combinatorial properties of algebraic matroids, Combinatorica 7, 39-48 (1987)]. We present a further step of generalization showing that a good characterization can also be obtained for the class of so-called pseudomodular matroids, introduced by A. Bj{\"o}rner and L. Lovász [Acta Sci. Math. 51, No. 3/4, 295-308 (1987)]. A small counterexample is included to show that pseudomodularity still does not cover all matroids that behave well with respect to matroid matching.", } @Article{zpr87-044, author = "M. Leclerc", institution = mi, title = "Eine Min-Max Beziehung f{\"u}r das Exakte Matroid Problem", journal = "Archiv der Mathematik", publisher = "Birkhäuser", volume = "49", pages = "103--105", year = "1987", keywords = "exact matroid problem, total dual integral system, matroid polytope of Edmonds and Giles; 05B35", annote = "Das Exakte Matroid-Problem ist: Gegeben sei ein Matroid M=(E,J), eine Teilmenge R von E und eine nat{\"u}rliche Zahl $\ell$; finde eine Basis B von M, so dass $\vert B\cap R\vert =\ell$ gilt. In der Arbeit wird eine Gleichung bewiesen, die das Maximum der R-Elemente in einer Basis in Beziehung zum Minimum der Summe der R{\"a}nge einer bestimmten {\"U}berdeckung von M setzt. Der Beweis beruht auf einer Charakterisierung des total dual ganzzahligen Systems f{\"u}r das Matroid-Polytop von Edmonds und Giles.", } @Article{zpr87-043, author = "B. Fa{\ss}bender", institution = mi, title = "On a generalization of a theorem of Nash-Williams", journal = "Journal of Combinatorial Theory B", volume = "52", number = "1", pages = "42--44", year = "1991", keywords = "theorem of Nash-Williams, Hamiltonian, minimum degree, independence number; 05C40, 05C45, 05C38", } @Article{zpr87-042, author = "M. Hofmeister", institution = mi, title = "Counting Double Covers of Graphs", journal = "Journal of Graph Theory", volume = "12", number = "3", pages = "437--444", year = "1988", keywords = "automorphism group, isomorphism, double covers; 05C30, 05C70, 05C25, 20B25", annote = "Any group of automorphisms of a graph G induces a notion of isomorphism between double covers of G. The corresponding isomorphism classes will be counted.", } @TechReport{zpr87-041, author = "M. Leclerc and C. H. C. Little and F. Rendl", institution = mi, title = "Constrained Matching Problems And Pfaffian Graphs", year = "1987", keywords = "multiple choice coloring, Pfaffian graphs, set partitioning;", annote = "We consider the problem of finding a perfect matching in a graph satisfying additional conditions which can be described as follows: for a number of subsets of edges the perfect matching is allowed to contain only a prescribed number of elements of each set. We show that this problem is polynomial for Pfaffian graphs. The recognition problem for general Pfaffian graphs is shown to be in NP. Moreover, a polynomial algorithm for recognizing bipartite Pfaffian graphs is provided.", } @Article{zpr87-040, author = "M. Leclerc and F. Rendl", institution = mi, title = "A Multiply Constrained Matroid Optimization Problem", journal = "Discrete Mathematics", volume = "73", number = "1/2", pages = "207--212", year = "1989", keywords = "matroids, multi-color matroid optimization problem, minimum cost basis, minimum spanning tree, minimum cost schedule, preprocessing phase; 90C27, 90B35, 05B35, 90C35", annote = "We consider the problem of finding a minimum weight basis of a matroid satisfying additional conditions which can be described as follows: each element of the matroid is assigned a color and feasible bases can use at most a prescribed number of elements from each color. This problem is a special case of weighted matroid intersection. We provide an algorithm for this problem which improves general matroid intersection algorithms by exploiting the simple structure of the side constraints.", } @Article{zpr87-039, author = "M. Hofmeister", institution = mi, title = "Spectral Radius and Degree Sequence", journal = "Mathematische Nachrichten", volume = "139", pages = "37--44", year = "1988", keywords = "spectral mean characteristic, degree sequence, spectral radius; 05C50", annote = "For a nonregular graph there is exactly one value of p such that the p-mean of its degree sequence is equal to the spectral radius. We try to investigate the structural content of this so-called spectral mean characteristic; in particular, we characterize the connected graphs of spectral mean characteristic 2.", } @Article{zpr86-037, author = "W. Nettekoven and W. Henke", institution = mi, title = "The Hypherbolic n-Space as a Graph in Euclidean (6n-6)Space", journal = "manuscripta mathematica", volume = "59", pages = "13--20", year = "1987", keywords = "hyperbolic space, Euclidean space, graphs, isometric imbedding; 53C40, 53A07", annote = "Let $H\sp n$ denote the n-dimensional hyperbolic space of constant curvature (-1) and $E\sp N$ the N-dimensional Euclidean space. {\it D. Blanusa} [Monatsh. Math. 59, 217-229 (1955; Zbl. 67, 144)] constructed an isometric $C\sp{\infty}$-imbedding $H\sp 2\to E\sp 6$ whose image is the graph of a $C\sp{\infty}$-map ${\bbfR}\sp 2\to {\bbfR}\sp 4$. For $n\ge 3$, in the same article, Blanusa was only able to construct a 1-1 isometric $C\sp{\infty}$-immersion $H\sp n\to E\sp{6n-5}$ which is not an imbedding in the strong sense (i.e. not a homeomorphism onto a topological subspace). The present paper generalizes the stronger 2- dimensional result of Blanusa. Theorem: For each $n\ge 2$, there exists an isometric $C\sp{\infty}$-imbedding $H\sp n\to E\sp{6n-6}$ whose image is the graph of a C-map ${\bbfR}\sp n\to {\bbfR}\sp{5n-6}$. Moreover explicit formulas are given which apply to the isometric imbedding problem for a larger class of Riemannian manifolds.", } @Article{zpr86-036, author = "D. Jungnickel and M. Leclerc", institution = mi, title = "The 2-Matching Lattice of a Graph", journal = "Journal of Combinatorial Theory B", volume = "46", number = "2", pages = "246--248", year = "1989", keywords = "lattice, perfect 2-matching, graphs, perfect matchings; 05C70, 06B20, 05C50, 05C99", annote = "We determine the lattice generated by the perfect 2-matchings of a graph in terms of the linear subspace of RE.", } @Article{zpr86-035, author = "C. Hohmann and W. Kern", institution = mi, title = "Optimization and Optimality Test for the Weighted Max-Cut problem", journal = "Zeitschrift f{\"u}r Operations Research", volume = "34", number = "3", pages = "195--206", year = "1990", keywords = "polynomial transformation, max-cut problem, polynomial equivalent optimality test, weighted case, rescaling, optimal testing oracle, binary search, unweighted case; 90C35, 90C60", annote = "The authors show that, for the weighted and unweighted version of the max-cut problem, there is a polynomial equivalent optimality test which improves a given suboptimal solution. For the weighted case, the proof uses rescaling techniques (for a given cut, the graph is modified by scaling the weight of the uncut edges by a factor 0 < lambda < 1) together with concurrent uses of an optimal testing oracle and binary search. As a corollary one gets, with the help of an optimality testing oracle, a polynomial-time heuristic for the weighted max-cut problem. For the unweighted case, the proof is much simpler, and the heuristic is now an exact algorithm. This implies that recognizing an optimal cut in an unweighted graph is NP-hard.", } @Article{zpr86-034, author = "M. Leclerc", institution = mi, title = "Optimization over a Slice of the Bipartite Matching Polytope", journal = "Discrete Mathematics", volume = "73", number = "1/2", pages = "159--162", year = "1989", keywords = "polynomial solution, exact perfect matching; 90C35, 05C70, 68Q25, 52B", annote = "We discuss a special case of the Exact Perfect Matching Problem, which is polynomially solvable. A good algorithm is given.", } @Article{zpr86-033, author = "W. Kern", institution = mi, title = "On the Depth of Combinatorial Optimization Problems", journal = "Discrete Applied Mathematics", volume = "43", number = "2", pages = "115--129", year = "1993", keywords = "hill climbing, depth, computational complexity, Simulated Annealing; 68Q25, 05C70, 94C10, 68R10", } @Article{zpr86-032, author = "M. Leclerc", institution = mi, title = "Slices of the Matching Polytopes", journal = "Mitteilungen des math. Seminars Gie{\"s}en", volume = "192", pages = "85--88", year = "1989", keywords = "polyhedral combinatorics, exact matching problem; 05C70, 52B", } @Article{zpr86-031, author = "W. Kern and A. Wanka", institution = mi, title = "On a Problem about Covering Lines by Squares", journal = "Discrete & Computational Geometry", volume = "5", number = "1", pages = "77--82", year = "1990", keywords = "covering lines by squares, distribution of points in a square; 52C17, 05B40", annote = "Let S be the square [0,n]2 of side length $n\in {\bf N}$ and let ${\cal S}=\{ S_1,\ldots,S_t\}$ be a set of unit squares lying inside S, whose sides are parallel to those of S. The set $\cal S$ is called a line cover, if every line intersecting S also intersects some $S_i\in {\cal S}$. Let $\tau (n)$ denote the minimum cardinality of a line cover, and let $\tau '(n)$ be defined in the same way, except that we restrict our attention to lines which are parallel to either one of the axes or one of the diagonals of S. It has been conjectured by L.F. Tóth that $\tau (n)=2n+0(1)$ and I.~Barányi and Z. Füredi that $\tau (n)={3\over 2}n+0(1)$. We will prove instead, $\tau '(n)={4\over 3}+0(1)$, and as to Tóth's conjecture, we will exhibit a ``non integer´´ solution to a related LP-relaxation, which has size equal to ${3\over 2}+0(1)$.", } @TechReport{zpr86-030, author = "Arbeitsgruppe Optimierung", institution = mi, title = "Arbeitsbericht 1985/86", year = "1986", } @TechReport{zpr86-029, author = "H.-J. Rieder", institution = mi, title = "On k-Tuple-Colorings of Graphs", year = "1986", annote = "This paper deals with (k:i)-colorings of graphs as introduced by Brigham and Dutton [Generalized k-tuple colorings of cycles and other graphs, J. Comb. Theory B 32, 90-94] as a generalization of Stahl's k-tuple-coloring [n-tuple colorings and associated graphs, J. Comb. Theory B 20, 185-203].
    A (k:i)-coloring is a generalized vertex coloring of a graph. A set of k colors is assigned to each vertex in such a way that any two adjacent vertices have exactly i coors in common.
    We will investigate the minimum number of colors required for (k:i)-colorings of wheels. In addition, we will give some counter-examples for a monotony-conjecture stated in [Generalized k-tuple colorings of cycles and other graphs, J. Comb. Theory B 32, 90-94].", } @Article{zpr86-028, author = "W. Kern", institution = mi, title = "A Probabilistic Analysis of the Switching Algorithm for the Euclidean {TSP}", journal = "Mathematical Programming (A)", volume = "44", number = "2", pages = "213--219", year = "1989", keywords = "Euclidean Traveling Salesman, probabilistic analysis, simulated annealing, k-switching algorithm; 90C35, 68Q25", annote = "The 2-switching Algorithm for the Euclidean Traveling Salesman problem is studied. A probabilistic analysis is developed. It gives an evaluation of a simulated annealing version of the Lin-Kernigham algorithm. A bound of the number of points n and the minimum distance d* between a tour sigma and that generated by switching points tau(sub i) and sigma(sub j) is defined. For small d*s the necessary computation can be too time-consuming. In order to prove a lemma, A sub(epsilon)(i,j,k) is fixed as the set of points x such that the absolute value of a function F(i,j,k,x) is bounded by an arbitrary epsilon > 0. The lemma establishes that this set is bounded and the bound is calculated. The behavior of a strategy for fixing paths is analyzed in a ``claim''. This claim is a corrollary to the lemma. It is proved and two figures illustrate the involved ideas. The probability that the algorithm stops after no more than O(n sup(18)) steps is 1 - (d(x,i) - d(x,j)). The possibility of developing a k-switching algorithm is sketched.", } @Article{zpr86-027, author = "A. Bachem and A. Wanka", institution = mi, title = "Matroids without Adjoint", journal = "Geometriae Dedicata", volume = "29", number = "3", pages = "311--315", month = mar, year = "1989", keywords = "rank-4 matroid, lattice of flats; 05B35", annote = "The purpose of this note is to give an example of a rank-4 matroid which not only shows that Levi's intersection property is not a sufficient condition for the existence of an adjoint but also seems to have an interesting structure of the lattice of flats.", } @Article{zpr86-026, author = "W. Kern", institution = mi, title = "On the Rate of Convergence of some Stochastic Processes", journal = "Mathematics of Operations Research", volume = "14", number = "2", pages = "275--280", month = may, year = "1989", keywords = "stochastic combinatorics, traveling salesman problem, bin-packing, convergence rates; 60F05, 68Q25, 05B40", annote = "Let X1,X2,... be i.i.d. random variables taking on values in Rd. For n >= 2, let Yn be a real-valued random variable which is measurable with respect to the sigma-algebra generated by X1,...,Xn. Let f:Rnd -> R be a Borel measurable function such that Yn = f(X1,...,Xn). Define ``missing one'' functions fn, i :R(n-1)d -> R by fni (x1,...,xn) = fn-1(x1,...,xi-1,xi+1,...,xn). Assume that \gamma (n) >= n. Under some conditions on fni the following main theorem holds: There exist constants alpha, beta > 0 such that for all n Prob(|Yn - EYn| > t) <= beta. e sup(-alpha t. sqrt(n / gamma (n))).", } @Article{zpr86-025, author = "A. Bachem and A. Wanka", institution = mi, title = "Euclidean Intersection Properties", journal = "Journal of Combinatorial Theory B", volume = "47", number = "1", pages = "10--19", month = aug, year = "1989", keywords = "Euclidean orientations, intersection properties, lattices, oriented matroids; 05B35", annote = "There are matroids which have Euclidean and non-Euclidean orientations and there are also matroids whose inherent structure does not allow any Euclidean orientation. In this paper we discuss some lattice theoretic properties of matroids which when used in an oriented version guarantee Euclideanness. These properties depend all on the existence of intersections of certain flats (which is equivalent to Euclideanness interpreted in the Las Vergnas notation of oriented matroids). We introduce three classes of matroids having various intersection properties and show that two of them cannot be characterized by excluding finitely many minors.", } @PhdThesis{zpr86-024, author = "A. Wanka", institution = mi, title = "Matroiderweiterungen zur Existenz endlicher {LP}-Algorithmen, von Hahn-Banach-{S}{\"a}tzen und Polarit{\"a}t in orientierten Matroiden", year = "1986", keywords = "extensions of matroids, finite LP-algorithms, Hahn-Banach theorems, polarity, oriented matroids; 05B35, 90C05", annote = "Hauptanliegen dieser Arbeit ist, verschiedene Schnittbedingungen in der (orientieren) Matroid-Theorie zu etablieren, durch unendlich viele verschiedene Matroide zu unterscheiden und diverse Folgerungen der einzelnen Schnittbedingungen fuer die Polyedertheorie orientierter Matroide abzuleiten.", } @Article{zpr85-023, author = "W. Kern", institution = mi, title = "On Finite Locally Projective Planar Spaces", journal = "Journal of Combinatorial Theory A", volume = "48", number = "2", pages = "247--254", month = jul, year = "1988", keywords = "finite planar space embeddable into a projective space; 51E20, 51A45, 05B35", annote = "Let L be a finite geometric lattice of rank 4 (i.e., a planar space) such that any two planes of L meet in a line. There is a longstanding conjecture due to W.M. Kantor which states that every such lattice can be embedded into a projective space. If L is given as above, then for every point p of L, L/p is a projective plane of order n (independent of p). Recently, A. Beutelspacher has shown that if L has at least n³ points then L can be embedded into a projective space. We give an alternative proof of his result, which applies to the more general class of finite locally projective planar spaces. Furthermore, our considerations lead to some more insight into the geometrical structure of a possible counterexample to Kantor's conjecture. For example, they can be used to show that the bound on n³ is not tight.", } @TechReport{zpr85-022, author = "J. Bokowski and B. Sturmfels", institution = mi, title = "Programmsystem zur Realisierung orientierter Matroide", year = "1985", annote = "Im Zusammenhang mit unseren Arbeiten
    • Oriented Matroids and Chirotops - Problems of Geometric Realizability
    • On the Coordinatization of Oriented Matroids
    • Polytopal and Nonpolytopal Spheres - An Algorithmic Approach
    entstand ein interaktives Programmsystem zur Bearbeitung von Chirotopen/orientierten Matroiden. Anhand einiger Beispiele sollen die vorliegenden Programme dokumentiert und damit auch gleichzeitig die in den o.a. Arbeiten beschriebenen algorithmischen Ans{\"a}tze n{\"a}her erl{\"a}utert werden. F{\"u}r den theoretischen Hintergrund der verwandten Begriffe und Verfahren sei neben diesen drei Arbeiten auf die dort zitierte Literatur verwiesen. Ein hier nicht beschriebenes Programm gestattet zus{\"a}tzlich die Auflistung aller (simplizialen) Chirotope, die gewisse verbotene Kreise nicht besitzen (Realisierung von kombinatoischen Mannigfaltigkeiten).", } @Article{zpr85-021, author = "J. Bokowski and B. Sturmfels", institution = mi, title = "On the Coordinatization of Oriented Matroids", journal = "Discrete & Computational Geometry", volume = "1", pages = "293--306", year = "1986", keywords = "realizability problems, oriented matroids, algorithm; 05B35", annote = "Several important and hard realizability problems of combinatorial geometry can be reduced to the realizability problem of oriented matroids. In this paper we describe a method to find a coordinatization for a large class of realizable cases. This algorithm has been used successfully to decide several geometric realizability problems. It is shown that all realizations found by our algorithm fulfill the isotopy property.", } @TechReport{zpr85-020, author = "W. Kern", institution = mi, title = "On Modular Embeddings of Geometric Lattices (Extended Abstract)", year = "1985", pages = "5", } @Article{zpr85-019, author = "A. Bachem and A. Wanka", institution = mi, title = "Separation Theorems for Oriented Matroids", journal = "Discrete Mathematics", volume = "70", number = "3", pages = "303--310", year = "1988", keywords = "Radon's theorem, Minty's lemma, Hahn-Banach theorem, Helly's theorem, oriented matroids; 05B35", annote = "In this paper we show that Minty's lemma can be used to prove the Hahn-Banach theorem as well as other theorems in this class such as Radon's and Helly's theorem for oriented matroids having an intersection property which guarantees that every pair of flats intersects in some point extension ${\cal O}\cup p$ of the oriented matroid ${\cal O}$.", } @Article{zpr85-018, author = "A. Bachem and W. Kern", institution = mi, title = "On Sticky Matroids", journal = "Discrete Mathematics", volume = "69", number = "1", pages = "11--18", year = "1988", keywords = "sticky geometric lattices, sticky uniform matroids; 05B35", annote = "The ``sticky conjecture'' states that a geometric lattice is modular if and only if any two of its extensions can be ``glued together''. It is known to be true as far as rank 3 geometries are concerned. In this paper we show that it is sufficient to consider a very restricted class of rank 4 geometries in order to settle the question. As a corollary we get a characterization of uniform sticky matroids, which has been found by Poljak and Turzik [Amalgamation over uniform matroids, Czech. Math. Journal 34, 109 (1984)].", } @Article{zpr85-017, author = "A. Bachem and A. Wanka", institution = mi, title = "On Intersection Properties of (Oriented) Matroids (Extended Abstract)", journal = "Methods of Operations Research", volume = "53", pages = "227--229", year = "1985", } @Article{zpr85-016, author = "W. Kern", institution = mi, title = "An Efficient Algorithm for Solving a Special Class of {LP}'s", journal = "Computing", volume = "37", number = "3", pages = "219--226", year = "1986", keywords = "0-1 matrix, Manhattan Skyline matrix; 65K05, 90C05", annote = "We consider LP's of the form max$\{$ cx$\vert \ell \le Ax\le b$, $L\le x\le U\}$ where l,b,L,U are nonnegative and A is a 0-1 matrix which looks like ``Manhattan Skyline''i.e. the support of each row is contained in the support of every subsequent row. An O(nm+n log n) algorithm is presented for solving the problem.", } @PhdThesis{zpr85-015, author = "W. Kern", institution = mi, title = "Verbandstheoretische Dualit{\"a}t in kombinatorischen Geometrien und orientierten Matroiden", year = "1985", pages = "57", keywords = "matroid, geometric lattice, oriented matroids, polyhedra, linear programming; 05B35", } @Book{zpr85-014, editor = "A. Bachem and H. W. Hamacher", institution = mi, title = "Applications of Combinatorial Methods in Mathematical Programming", note = "Papers from the Joint US/FRG Seminar held in Gainesville, Fla., March 18--22, 1985, Discrete Appl. Math. 15 (1986), no. 2-3", publisher = "North-Holland", year = "1986", pages = "i--ii and 121--378", } @Article{zpr85-013, author = "R. Euler and A. R. Mahjoub", institution = mi, title = "On a Composition of Independence Systems by Circuit Identification", journal = "Journal of Combinatorial Theory B", volume = "53", number = "2", pages = "235--259", year = "1991", keywords = "independence systems, independent set problem, convex hull, incidence vectors, polytope; 05D05, 52B05 , 05C99", annote = "Call an independence system (E,I) linearly relaxable, if the circuit-inequalities x(C) <= |C|-1 together with the constraints 0 <= xe <= 1 for all e in E are sufficient to define P(I), the convex hull of the incedence vectors of members of I. Examples are given by independence systems associated with bipartite subgraphs of graphs not contractible to K5, cf. J. Fonlupt et al. [Compositions of graphs and the bipartite subgraph polytope, Tech.Rep. 459, IMAG-Artemis (1984)], or with acyclic subdigraphs of digraphs obtainable from graphs not contractible to K3,3, cf. F. Barahona and A.R. Mahjoub [Compositions in the acyclic subdigraph polytope, Tech.Rep. 500, IMAG-Artemis (1985)]. Further classes are stable set independence systems of bipartite graphs and, as we are going to show here, a generalization of these within the framework of balanced matrices.
    The composition of bipartite subgraph resp. acyclic subdigraph independence systems and in particular of their associated polyhedra by the identification of a pair of 3-cycles, resp. 2-dicycles together with its implications for an algorithmic treatment has been the central subject of the above mentioned two references. We generalize this kind of composition within the framework of independence systems satisfying a special circuit-exchange property and discuss its implications for the associated polyhedra, totally dual integral linear systems describing these as well as relaxed optimization problems. Special attention is given to the linearly relaxable such independence systems.", } @InCollection{zpr85-012, author = "A. Bachem", institution = mi, title = "Dualit{\"a}t und Polarit{\"a}t in diskreten Strukturen", booktitle = "{\"O}konomische Prognose - Entscheidungs- und Gleichgewichtsmodelle", editor = "W. Krelle", publisher = "VHC Verlag", year = "1986", } @Article{zpr84-011, author = "U. Zimmermann", institution = mi, title = "Duality for Balanced Submodular Flows", journal = "Discrete Applied Mathematics", volume = "15", pages = "365--376", year = "1986", keywords = "duality, balanced flow problems, balanced submodular flow, polynomial complexity bounds; 90B10, 68Q25", annote = "Balanced submodular flows generalize balanced flows as introduced by M. Minoux [Flots équilibrés et flots avec sécurité, Bull. Direction Études Recherches Sér. C. Math. Informat., 5-16 (1976)] in the discussion of reliability and security problems. We develop a dual method for optimization in totally ordered sets which yields a genuinely polynomial method for solving maximum balanced flow problems. For solving maximum balanced submodular flow problems the same approach leads to a method of genuinely polynomial complexity modulo the complexity of submodular function minimization.", } @TechReport{zpr84-010, author = "U. Zimmermann", institution = mi, title = "Submodulare Fl{\"u}sse: Verfahren zur Minimierung linearer Zielfunktionen", year = "1984", keywords = "algebraic and algorithmic aspects, submodular flow problem, module-valued submodular flows, primal-dual method strong duality theorem in arbitrary modules; 90C10, 90C35, 90B10", annote = "We survey algebraic and algorithmic aspects of the submodular flow problem. After some motivating remarks on the usual network flow problem module-valued submodular flows are discussed. Main emphasis lies on a combinatorial development of the primal-dual method (potential method) of Cunningham and Frank in arbitrary modules. That approach enables the proof of a strong duality theorem in arbitrary modules. Finally, a comprehensive list of references is included.", } @InCollection{zpr84-009, author = "A. Bachem", title = "Optimization and Geometry in Discrete Structures", booktitle = "Convexity and its Applications", editor = "P. M. Gruber and J. M. Wills", institution = mi, year = "1983", pages = "9--29", publisher = "Birkh{\"a}user Verlag", keywords = "oriented matroids, convexity theorems, duality theorems; 05B35, 52B, 90C05, 05-02, 90-02", annote = "The purpose of this paper is to provide a short summary of some recent developments in the geometry of discrete structures. Clearly choosing topics of such an exposition the author's personal taste has played an important role. The emphasis lies on oriented matroid theory.
    The survey starts with a brief introduction into the theory of computational complexity explaining the meaning of ``easy'', ``hard'' and ``intractable'' problems. While emphasizing the role of a duality theory for developing efficient algorithms the rest of the paper considers oriented matroids from a linear programming point of view.", } @Article{zpr84-008, author = "I. S. Schubert and U. Zimmermann", institution = mi, title = "Nonlinear One-Parametric Bottleneck Linear Programming", journal = "Zeitschrift f{\"u}r Operations Research A", volume = "29", number = "5", pages = "187--201", year = "1985", keywords = "one-parametric linear bottleneck problem, linear constraints; 90C31", annote = "We consider the one-parametric linear bottleneck problem min{c(x,t)| x in P(t)} where the bottleneck objective c(x,t):= max{cj(t) | xj>0} is minimized subject to linear constraints, i.e. P(t):={x| A(t)x=b(t), x>=0}. All coefficients are assumed to be continuous functions of one real parameter t which varies in a real interval S. A method is developed for constructing a partition of S into subintervals on which either a basis stays optimal or the problem stays infeasible. Finiteness of the partition is due to certain finiteness assumptions on the zeros of particular combinations of the coefficient functions. Using a lexicographic refinement of the objective function a characterization of the optimality interval of a fixed basis is derived which is independent on explicit information about other bases.", } @TechReport{zpr84-007, author = "I. S. Schubert and U. Zimmermann", institution = mi, title = "One-Parametric Bottleneck Transportation Problems", year = "1984", annote = "We discuss the bottleneck transportation problem with one nonlinear parameter in the bottleneck objective function. A finite sequence of feasible basic solutions which are optimal in subsequent closed parameter-intervals is generated using a primal method for the nonparametric subproblems. The best among three primal codes for solving those subproblems is selected based on extensive computational comparisons. We discuss computational experience with the sequential method for the case of linear and quadratic dependence on one parameter. Observed computational behaviour is O((nm)a) with a <=2.", } @TechReport{zpr84-006, author = "A. Bachem and R. Kannan", institution = mi, title = "Lattices and Basis Reduction Algorithm", year = "1984", annote = "The purpose of this paper is to introduce lattices, describe basic algorithms that deal with them and present an expository, but complete version of the elegant basis reduction algorithm due to A.K. Lenstra, H.W. Lenstra and L. Lovász [Factoring polynomials with rational coefficients, Mathematische Annalen 261, 513-534 (1982)]. Section 1 presents definitions and basic concepts followed by a basis reduction algorithm in 2 dimension which Gauss formulated in a different form. The Lenstra, Lenstra and Lovász Algorithm specializes to this in 2 dimensions. Section 3 presents the general basis reduction algorithm and a proof of its polynomial time boundedness. Section 4 contains our remarks on the algorithm and the appendix provides a verbatim description of Gauss' algorithm and a proof that the 3 dimensional algorithm of section 2 (which we name the 60° algorithm) is equivalent to it.", } @Article{zpr84-005, author = "A. Bachem and W. Kern", institution = mi, title = "Extension Equivalence of Oriented Matroids", journal = "European Journal of Combinatorics", volume = "7", pages = "193--197", year = "1986", keywords = "point extensions, matroids, extension lattice, extension equivalence, oriented matroids; 05B35, 06A06", annote = "The point extensions of a matroid M are in one-to-one correspondence to the set of all linear subclasses of M which, ordered by inclusion, form the so called extension lattice of M. Two matroids are said to be extension equivalent if their extension lattices are isomorphic. In this paper we show that for two extension equivalent (oriented) matroids M, and M' of equal rank M* is an adjoint of M iff M* is an adjoint of M' and use this result to prove: M is represetable over the field F if and only if M' is.", } @Article{zpr84-004, author = "R. Euler and R. E. Burkard and R. Grommes", institution = mi, title = "On Latin Squares and the Facial Structure of Related Polytopes", journal = "Discrete Mathematics", volume = "62", number = "2", pages = "155--181", year = "1986", keywords = "polytope, clutter, Latin squares; 05B15, 05B35", annote = "By identifying all latin squares of order n with certain n²-element subsets of an n³-element ground set En a clutter Bn is obtained, which induces an independence system (En,In) in a natural way. Starting from Ryser's conditions for the completion of latin rectangles, cf. L. Mirsky [Transversal Theory, Academic Press (1971)], we present special cases of circuits of (En,In) and extend Ryser's conditions slightly.
    Latin squares of order n correspond to the solutions of planar 3-dimensional assignment problems and, in view of its solution via linear programming techniques, we present some first classes of facet-defining inequalities for P(In) resp. P(In), the convex hull of all those 0-1 vectors, which correspond to members of In resp. Bn.", } @Article{zpr84-003, author = "U. Zimmermann", institution = mi, title = "Linear and Combinatorial Sharing Problems", journal = "Discrete Applied Mathematics", volume = "15", number = "1", pages = "85--104", year = "1986", keywords = "sharing problem, threshold techniques, knapsack sharing, group-valued submodular flow sharing, perfect b-matching, sharing polynomial complexity; 90C27, 68Q25", annote = "Sharing problems are minimax problems with separable objective, i.e. min {F(x) | x in P} where F(x) := max {fi(xi) | j=1,...,n}. For quasiconvex and lower semicontinuous functions fi on arbitrary totally ordered sets, we derive a duality theory. In particular, a general dual method is shown to apply to linear, combinatorial and convex sharing problems. For linear and bottleneck share functions fi the method is polynomially bounded in many applications.", } @Article{zpr84-002b, author = "A. Bachem and R. Euler", institution = mi, title = "Recent Trends in Combinatorial Optimization, {II}.", journal = "Chinese Journal of Operations Research", volume = "6", number = "1", pages = "21--36", year = "1987", annote = "This is part II of the Chinese translation of zpr84-002", } @Article{zpr84-002a, author = "A. Bachem and R. Euler", institution = mi, title = "Recent Trends in Combinatorial Optimization, {I}.", journal = "Chinese Journal of Operations Research", volume = "5", number = "2", pages = "18--28", year = "1986", annote = "This is part I of the Chinese translation of zpr84-002", } @Article{zpr84-002, author = "A. Bachem and R. Euler", institution = mi, title = "Recent Trends in Combinatorial Optimization", journal = "OR Spektrum", volume = "6", pages = "1--21", year = "1984", keywords = "combinatorial optimization, complexity theory, matroids, matching, network-flow, submodular functions, heuristic algorithms; 90C10, 90-02, 68Q25, 52B, 05B35", annote = "We survey important parts of the theory of combinatorial optimization as it is developed today. The emphasis lies on new theoretical results, which have proven useful in practical applications. In Section 2 we present some examples and explain our basic notation. The purpose of Section 3 is to introduce central concepts of complexity theory, in particular the notions of easy and hard problems. Starting from matroid, matching and network flow problems we describe how polynomially solvable generalizations of these can be obtained, taking account of the theory of submodular functions as a general framework. Oriented matroids as a suitable concept by which to generalize the theory of convex polyhedra in a purely combinatorial setting are discussed in the first part of a section on polyhedral theory. Part 2 is concerned with the relations between linear systems and combinatorics, in particular integer polyhedra. The structure and evaluation of heuristic algorithms is the subject of Section 6. Finally, we describe basic ideas for the solution of hard optimization problems as they have proven efficient for particular problem classes.", } @Article{zpr84-001, author = "A. Bachem and W. Kern", institution = mi, title = "Adjoints of Oriented Matroids", journal = "Combinatorica", volume = "6", number = "4", pages = "299--308", year = "1986", keywords = "geometric lattice, oriented matroids; 05B35", annote = "An adjoint of a geometric lattice G is a geometric lattice $\tilde G$ of the same rank into which there is an embedding e mapping the copoints of G onto the points of $\tilde G.$ In this paper we introduce oriented adjoints and prove that they can be embedded into the extension lattice of oriented matroids.", }