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 k 1 − 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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Knauer, C., Schramm, É., Spillner, A., Wolff, A. (2005). Configurations with Few Crossings in Topological Graphs. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_61
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DOI: https://doi.org/10.1007/11602613_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30935-2
Online ISBN: 978-3-540-32426-3
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