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BIT Numerical Mathematics

, Volume 33, Issue 4, pp 580–595 | Cite as

The complexity of detecting crossingfree configurations in the plane

  • Klaus Jansen
  • Gerhard J. Woeginger
Part I Computer Science

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.

AMS categories

05C05 68Q25 68R10 

Keywords

algorithmic complexity planar layouts geometry 

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Copyright information

© the BIT Foundation 1993

Authors and Affiliations

  • Klaus Jansen
    • 1
    • 2
  • Gerhard J. Woeginger
    • 1
    • 2
  1. 1.Fachbereich IV, Mathematik und InformatikUniversität TrierTrierGermany
  2. 2.Institut für InformationsverarbeitungTechnische Universität GrazGrazAustria

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