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The complexity of detecting crossingfree configurations in the plane

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Abstract

The computational complexity of the following type of problem is studied. Given a geometric graphG=(P, S) whereP is a set of points in the Euclidean plane andS a set of straight (closed) line segments between pairs of points inP, we want to know whetherG possesses a crossingfree subgraph of a special type. We analyze the problem of detecting crossingfree spanning trees, one factors and two factors in the plane. We also consider special restrictions on the slopes and on the lengths of the edges in the subgraphs.

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Authors and Affiliations

  1. Fachbereich IV, Mathematik und Informatik, Universität Trier, Postfach 3825, W-5500, Trier, Germany

    Klaus Jansen & Gerhard J. Woeginger

  2. Institut für Informationsverarbeitung, Technische Universität Graz, Klosterwiesgasse 32/II, A-8010, Graz, Austria

    Klaus Jansen & Gerhard J. Woeginger

Authors
  1. Klaus Jansen
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  2. Gerhard J. Woeginger
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Additional information

Klaus Jansen acknowledges support by the Deutsche Forschungsgemeinschaft. Gerhard J. Woeginger acknowledges support by the Christian Doppler Laboratorium für Diskrete Optimierung.

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Jansen, K., Woeginger, G.J. The complexity of detecting crossingfree configurations in the plane. BIT 33, 580–595 (1993). https://doi.org/10.1007/BF01990536

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  • DOI: https://doi.org/10.1007/BF01990536

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