Configurations with few crossings in topological graphs

Authors:
Christian Knauer;Étienne Schramm;Andreas Spillner;Alexander Wolff
Affiliations:
Institute of Computer Science, Freie Universität Berlin;Fakultät für Informatik, Universität Karlsruhe, Karlsruhe;Institute of Computer Science, Friedrich-Schiller-Universität Jena;Fakultät für Informatik, Universität Karlsruhe, Karlsruhe
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

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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 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.