Configurations with Few Crossings in Topological Graphs

  • Christian Knauer
  • Étienne Schramm
  • Andreas Spillner
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)


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, st paths, cycles, matchings, and κ-factors for κ ∈ {1,2}. We show that it is NP-hard to approximate the minimum number of crossings for these configurations within a factor of k1 − ε for any ε > 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Christian Knauer
    • 1
  • Étienne Schramm
    • 2
  • Andreas Spillner
    • 3
  • Alexander Wolff
    • 2
  1. 1.Institute of Computer ScienceFreie Universität Berlin 
  2. 2.Fakultät für InformatikUniversität KarlsruheKarlsruhe
  3. 3.Institute of Computer ScienceFriedrich-Schiller-Universität Jena 

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