computer science publication server: No conditions. Results ordered -Date Deposited. 2021-04-22T23:13:07ZEPrintshttp://e-archive.informatik.uni-koeln.de/images/sitelogo.pnghttp://e-archive.informatik.uni-koeln.de/2015-10-16T08:24:15Z2016-04-08T08:29:29Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/889This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/8892015-10-16T08:24:15ZA practical mixed-integer programming model for
the vertex separation number problemWe present a novel mixed-integer programming formulation for the vertex separation number problem in general directed graphs. The model is conceptually simple and, to the best of our knowledge, much more compact than existing ones. First experiments give hope that it can solve larger instances than has been possible so far if it is combined with preprocessing techniques to reduce the search space.Sven MallachMallach, Sven2014-06-30T12:46:47Z2014-06-30T12:46:47Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/752This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/7522014-06-30T12:46:47ZA survey on oracle techniquesBernhard KorteKorte, BernhardRainer SchraderSchrader, Rainer2014-06-30T12:33:44Z2014-06-30T12:33:44Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/740This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/7402014-06-30T12:33:44ZGraphs and OrdersUlrich FaigleFaigle, UlrichRainer SchraderSchrader, Rainer2010-09-28T10:19:04Z2014-07-04T09:32:28Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/850This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/8502010-09-28T10:19:04ZAcyclic Subdigraphs and Linear Orderings: Polytopes, Facets, and a cutting Plane AlgorithmMartin GrötschelGrötschel, MartinMichael JüngerJünger, MichaelGerhard ReineltReinelt, Gerhard2010-09-01T12:37:08Z2014-07-04T09:32:11Zhttp://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, Gerhard2010-09-01T12:35:22Z2014-07-04T09:33:01Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/816This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/8162010-09-01T12:35:22ZFacets of the Linear Ordering Polytope Martin GrötschelGrötschel, MartinMichael JüngerJünger, MichaelGerhard ReineltReinelt, Gerhard2008-10-24T00:00:00Z2011-12-19T09:44:30Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/580This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5802008-10-24T00:00:00ZSchranken für den minimalen orientierten DurchmesserIn this thesis, we consider the problem of finding an orientation of an undirected graph with minimal diameter. We show a relation between the minimum oriented diameter diam_{min}(G) of an undirected graph and the size gamma(G) of a minimal dominating set, which improves an upper bound discovered by Fomin et al. We show if G is a strongly connected graph, then: diam_{min}(G)leq 4gamma(G). Furthermore, if we have a graph G and a dominating set D , not necessarily a minimal dominating set of G , we show how to construct an orientation H of G in polynomial time fulfilling diam(H)leq 4|D|. Furthermore, we determine the exact upper bound for {C_3,C_4} -free graphs. If G is a strongly connected {C_3,C_4} -free graph, then the following holds: diam_{min}(G)leq 3gamma(G)+1. We consider bidirected graphs and characterize undirected graphs that allow a strongly connected bidirection. We show, that for those graphs a bidirected orientation ar{H} exist with diam(ar{H})leq 10gamma(ar{H})-5 .Martin LätschLätsch, Martin2008-07-30T00:00:00Z2012-01-12T09:15:28Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/493This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4932008-07-30T00:00:00ZBimodal Crossing MinimizationWe consider the problem of drawing a directed graph in two dimensions with a small or minimum number of crossings such that for every node the incoming (and hence the outgoing) edges appear consecutively in the cyclic adjacency lists. We show how to adapt the planarization method and the recently devised exact crossing minimization approach in a simple way. We report experimental results on the increase in the number of crossings involved by this additional restriction on the set of feasible drawings. It turns out that this increase is negligible for most practical instances.Christoph BuchheimBuchheim, ChristophMichael JüngerJünger, MichaelAnnette MenzeMenze, AnnetteMerijam PercanPercan, Merijam2008-03-10T00:00:00Z2012-01-09T16:54:30Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/559This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5592008-03-10T00:00:00ZDrawing cycles in networksIn this paper we show how a graph that contains a specified cycle can be drawn in the plane such that the cycle is drawn circularly while the rest of the graph is layouted orthogonally. We also show how to extend this algorithm to deal with a set of disjoint cycles at once.Christoph BuchheimBuchheim, ChristophMichael JüngerJünger, MichaelMerijam PercanPercan, MerijamMichael SchulzSchulz, MichaelChristina ThelenThelen, Christina2007-12-07T00:00:00Z2012-01-09T16:53:23Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/566This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5662007-12-07T00:00:00ZPlanarization With Fixed Subgraph EmbeddingThe visualization of metabolic networks using techniques of graph drawing has recently become an important research area. In order to ease the analysis of these networks, readable layouts are required in which certain known network components are easily recognizable. In general, the topology of the drawings produced by traditional graph drawing algorithms does not reflect the biologists' expert knowledge on particular substructures of the underlying network. To deal with this problem we present a constrained planarization method---an algorithm which computes a graph layout in the plane preserving the predefined shape for the specified substructures while minimizing the overall number of edge-crossings.Christoph BuchheimBuchheim, ChristophMichael JüngerJünger, MichaelMaria KandybaKandyba, MariaMerijam PercanPercan, MerijamMichael SchulzSchulz, Michael2007-12-04T00:00:00Z2011-12-19T09:44:37Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/562This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5622007-12-04T00:00:00ZLightness of digraphs in surfaces and directed game chromatic numberThe lightness of a digraph is the minimum arc value, where the value of an arc is the maximum of the in-degrees of its terminal vertices. We determine upper bounds for the lightness of simple digraphs with minimum in-degree at least 1 (resp., graphs with minimum degree at least 2) and a given girth k, and without 4-cycles, which can be embedded in a surface S. (Graphs are considered as digraphs each arc having a parallel arc of opposite direction.) In case k is at least 5, these bounds are tight for surfaces of nonnegative Euler characteristics. This generalizes results of He et al. [11] concerning the lightness of planar graphs. From these bounds we obtain directly new bounds for the game coloring number, and thus for the game chromatic number of (di)graphs with girth k and without 4-cycles embeddable in S. The game chromatic resp. game coloring number were introduced by Bodlaender [3] resp Zhu [22] for graphs. We generalize these notions to arbitrary digraphs. We prove that the game coloring number of a directed simple forest is at most 3.Dominique AndresAndres, Dominique2006-02-08T00:00:00Z2012-01-09T16:17:35Zhttp://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, Britta2004-12-13T00:00:00Z2011-12-19T09:44:46Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/474This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4742004-12-13T00:00:00ZSpieltheoretische Kantenfärbungsprobleme auf Wäldern und verwandte StrukturenThis diploma thesis discusses graph colouring games, as introduced by Bodlaender [3], in a more general setting. The main results are: The directed and undirected game chromatic indices of the class of forests of maximum degree D are D+1, for D=3, D=5, and D>5. The directed game chromatic indices of the class of forests of maximum degree 2 are 2 or 3, depending on whether passing is allowed for Alice in the underlying game. The method of decomposition of independent subtrees is extended from edge colouring games to node colouring games and leads to new proofs resp. new results concerning the undirected resp. directed (new) game chromatic numbers of the class of forests. These numbers are 4 (3) resp. 3 (3). The results mentioned so far are also true for infinite instead of finite graphs. Some general properties of graph colouring games are examined. A list of important open questions can be found at the end.Dominique AndresAndres, Dominique2001-04-02T00:00:00Z2011-12-19T09:45:09Zhttp://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, Ewald