Configurations with few crossings in topological graphs

C. Knauer, É. Schramm, A. Spillner, A. Wolff

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    2 Citations (Scopus)

    Abstract

    In this paper we study the problem of computing subgraphs of a certain configuration in a given topological graph G such that the number of crossings in the subgraph is minimum. The configurations that we consider are spanning trees, s–t paths, cycles, matchings, and ¿-factors for ¿ ¿ {1,2}. We show that it is NP-hard to approximate the minimum number of crossings for these configurations within a factor of k 1¿-¿e for any e > 0, where k is the number of crossings in G. We then show that the problems are fixed-parameter tractable if we use the number of crossings in the given graph as the parameter. Finally we present a simple but effective heuristic for spanning trees.
    Original languageEnglish
    Title of host publicationAlgorithms and computation : 16th international symposium, ISAAC2005, Sanya, Hainan, China, December 19-21, 2005 : proceedings
    EditorsX. Deng, D.Z. Du
    Place of PublicationBerlin
    PublisherSpringer
    Pages604-613
    ISBN (Print)3-540-30935-7
    DOIs
    Publication statusPublished - 2005

    Publication series

    NameLecture Notes in Computer Science
    Volume3827
    ISSN (Print)0302-9743

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