computer science publication server: No conditions. Results ordered -Date Deposited. 2021-04-22T23:59:47ZEPrintshttp://e-archive.informatik.uni-koeln.de/images/sitelogo.pnghttp://e-archive.informatik.uni-koeln.de/2010-09-01T12:37:08Z2014-07-04T09:32:11Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/815This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/8152010-09-01T12:37:08ZOn the acyclic Subgraph Polytope Martin GrötschelGrötschel, MartinMichael JüngerJünger, MichaelGerhard ReineltReinelt, Gerhard2010-08-31T14:44:59Z2014-07-04T09:31:10Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/814This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/8142010-08-31T14:44:59ZGeneralizations of Cliques, Odd Cycles and Anticycles and their relation to Independence System Polyhedra.Padberg [1973] has shown that if a graph G with vertex set V constitutes a clique (odd cycle, odd anticycle), then the inequality Σ[sub x, ∈, V] x[sub v] ≤ 1 (Σ [sub x, ∈ V] x[sub v] ≤ ½(|V| - 1), Σ[sub x, ∈, V] x[sub v] ≤ 2) defines a facet of P(G[sub ST](G)), the convex hull of the incidence vectors of stable sets in G. We generalize the concepts of cliques, odd cycles and anticycles to arbitrary independence systems (E, G) and show that the corresponding inequalities define facets of P(G), the convex hull of the incidence vectors of independent sets.Reinhardt EulerEuler, ReinhardtMichael JüngerJünger, MichaelGerhard ReineltReinelt, Gerhard2006-05-09T00:00:00Z2012-01-12T10:03:33Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/514This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5142006-05-09T00:00:00ZSubgraph characterization of Red/Blue-split graphs and König-Egerváry graphsKönig-Egerváry graphs (KEGs) are the graphs whose maximum size of a matching is equal to the minimum size of a vertex cover. We give an excluded subgraph characterization of KEGs. We show that KEGs are a special case of a more general class of graph: emph{Red/Blue-split} graphs, and give an excluded subgraph characterization of Red/Blue-split graphs. We show several consequences of this result including theorems of Deming-Sterboul, Lovász, and Földes-Hammer. A refined result of Schrijver on the integral solution of certain systems of linear inequalities is also given through the result on the weighted version of Red/Blue-split graphs.Ephraim KorachKorach, EphraimThành NguyenNguyen, ThànhBritta PeisPeis, Britta2006-02-08T00:00:00Z2012-01-09T16:17:35Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/515This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5152006-02-08T00:00:00ZOn a relation between the domination number and a strongly connected bidirection of an undirected graphAs a generalization of directed and undirected graphs, Edmonds and Johnson introduced bidirected graphs. A bidirected graph is a graph each arc of which has either two positive end-vertices (tails), two negative end-vertices (heads), or one positive end-vertex (tail) and one negative end-vertex (head). We extend the notion of directed paths, distance, diameter and strong connectivity from directed to bidirected graphs and characterize those undirected graphs that allow a strongly connected bidirection. Considering the problem of finding the minimum diameter of all strongly connected bidirections of a given undirected graph, we generalize a result of Fomin et al. about directed graphs and obtain an upper bound for the minimum diameter which depends on the minimum size of a dominating set and the number of bridges in the undirected graph.Martin LätschLätsch, MartinBritta PeisPeis, Britta2001-10-28T00:00:00Z2011-12-19T09:44:46Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/423This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4232001-10-28T00:00:00ZRouting with ReloadsWe examine routing problems with reloads, how they can be modeled, their properties and how they can be solved. We propose a simple model, the Pickup and Delivery Problem with Reloads (RPDP), that captures the process of reloading and can be extended for real world applications. We present results that show that the RPDP is solvable in polynomial time if the number of requests is bounded by a constant. Additionally, we examine a special case of the RPDP, the k-Star Hub Problem. This problem is solvable efficiently by network flow approaches if no more than two hubs are available. Otherwise, it is NP-complete. In the second part of this thesis, additional constraints are incorporated into the model and a tabu search heuristic for this problem is presented. The heuristic has been implemented and tested on several benchmarking instances, both artificial and a real-world application. In the appendix, we discuss the application of column generation for a reload problem.Peter OertelOertel, Peter2001-04-02T00:00:00Z2011-12-19T09:44:59Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/286This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/2862001-04-02T00:00:00ZMenger's Theorem as Morphism DualityThe 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). Winfried HochstättlerHochstättler, WinfriedJaroslav NesetrilNesetril, Jaroslav2001-04-02T00:00:00Z2012-01-09T11:50:36Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/98001This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/980012001-04-02T00:00:00ZOn the complexity of the disjoint paths problem (Extended abstract)Matthias MiddendorfMiddendorf, MatthiasFrank PfeifferPfeiffer, Frank2001-04-02T00:00:00Z2011-12-19T09:45:09Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/287This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/2872001-04-02T00:00:00ZOn computing all minimal solutions for feedback problemsWe 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|).B. SchwikowskiSchwikowski, B.Ewald SpeckenmeyerSpeckenmeyer, Ewald2001-04-02T00:00:00Z2011-10-24T09:04:24Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/43This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/432001-04-02T00:00:00ZOn a generalization of a theorem of Nash-WilliamsBert FaßbenderFaßbender, Bert2001-04-02T00:00:00Z2011-10-24T14:13:11Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/57This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/572001-04-02T00:00:00ZOn Longest Cycles and Strongly Linking Vertex SetsLet 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.Bert FaßbenderFaßbender, Bert2001-04-02T00:00:00Z2012-01-19T11:30:49Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/98This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/982001-04-02T00:00:00ZOn the Complexity of the Disjoint Path ProblemWe 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 e 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 e 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.Matthias MiddendorfMiddendorf, MatthiasFrank PfeifferPfeiffer, Frank2001-04-02T00:00:00Z2012-01-09T11:51:00Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/103This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/1032001-04-02T00:00:00ZThe Paths-Selection-ProblemLet 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 'Èulerian disjoint-paths problem'' are considered, and shown to be NP-complete as well.Matthias MiddendorfMiddendorf, MatthiasFrank PfeifferPfeiffer, Frank2001-04-02T00:00:00Z2011-12-19T09:46:22Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/343This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/3432001-04-02T00:00:00ZA Note on MaxFlow-MinCut and Homomorphic Equivalence in MatroidsThis 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.Winfried HochstättlerHochstättler, WinfriedJaroslav NesetrilNesetril, Jaroslav2001-04-02T00:00:00Z2011-10-24T14:10:48Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/46This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/462001-04-02T00:00:00ZKriterien vom Ore-Typ für längste Kreise in 2-zusammenhängenden GraphenLet G be a simple 2-connected graph of order u such that the degree-sum of any two nonadjacent vertices is at least {2 over 3} u, 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.Bert FaßbenderFaßbender, Bert2001-04-02T00:00:00Z2011-10-20T15:17:15Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/88This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/882001-04-02T00:00:00ZNon-Equivalent Cocycles of Graphs over Finite FieldsThe 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.Michael HofmeisterHofmeister, Michael2001-04-02T00:00:00Z2012-01-19T09:47:05Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/277This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/2772001-04-02T00:00:00ZOn the scheduling of one-dimensional transport systemsIn 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.Udo HeinrichsHeinrichs, UdoChristoph MollMoll, Christoph2001-04-02T00:00:00Z2011-12-19T09:46:39Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/282This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/2822001-04-02T00:00:00ZLarge Circuits in Binary Matroids of Large Cogirth: IILet 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.Winfried HochstättlerHochstättler, WinfriedBill JacksonJackson, Bill2001-04-02T00:00:00Z2012-01-19T09:49:16Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/220This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/2202001-04-02T00:00:00ZOptimale Linienführung und Routenplanung in VerkehrssystemenThis 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.Achim BachemBachem, AchimAnja HamacherHamacher, AnjaChristoph MollMoll, ChristophGuido RaspelRaspel, Guido2001-04-02T00:00:00Z2012-01-16T14:46:27Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/342This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/3422001-04-02T00:00:00ZSteiner-DiagramsIn 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.Ulrich BlasumBlasum, UlrichWinfried HochstättlerHochstättler, WinfriedPeter OertelOertel, Peter2001-04-02T00:00:00Z2011-12-19T09:45:31Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/192This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/1922001-04-02T00:00:00ZDas inverse Kürzeste-Wege-ProblemIn der Arbeit wird die Frage untersucht, was man für Aussagen über die Gewichte eines Graphen machen kann, wenn man die Kanten des Graphen und Distanzen zwischen einzelnen Knoten kennt. Die Arbeit umfaßt einige Vollständigkeitsaussagen. Außerdem wird der Zusammenhang zwischen Mehrgüterflußproblemen und dem inversen Kürzeste-Wege-Problem aufgearbeitet. Desweiteren umfaßt die Arbeit zusammenfassende Kapitel zur Komplexitätstheorie und zur Linearen Programmierung, die der Autor gerade auch für Nicht-Profis geschrieben hat.Christoph MollMoll, Christoph2001-04-02T00:00:00Z2012-01-16T13:49:12Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/385This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/3852001-04-02T00:00:00ZThe 5-Star-Hub-Problem is NP-completeIn this report we present a partial solution of the problems we left open in 99-384. We show that the 5-Star-Hub-Problem is NP-complete.Winfried HochstättlerHochstättler, WinfriedPeter OertelOertel, Peter