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


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 


algorithmic complexity planar layouts geometry 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. R. Garey and D. S. Johnson,Computers and Intractability, A Guide to the Theory of NP-completeness, Freeman, San Francisco, 1979.Google Scholar
  2. 2.
    J. Kratochvil, A. Lubiw and J. Nešetřil,Noncrossing subgraphs in topological layouts, SIAM J. Disc. Math. 4, 1991, 223–244.Google Scholar
  3. 3.
    T. Lengauer,Combinatorial Algorithms for Integrated Circuit Layout, Wiley-Teubner, New York, 1990.Google Scholar
  4. 4.
    F. Rendl and G. J. Woeginger,Reconstructing sets of orthogonal line segments in the plane, to appear in Discr. Math.Google Scholar
  5. 5.
    P. Rosenstiehl and R. E. Tarjan,Rectilinear planar layout of planar graphs and bipolar orientations, Discr. Comp. Geometry 1, 1986, 343–353.Google Scholar
  6. 6.
    P. J. Slater, E. J. Cockayne and S. T. Hedetniemi,Information dissemination in trees, SIAM J. Comput. 10 (1981), 692–701.Google Scholar
  7. 7.
    G. Toussaint,Pattern recognition and geometrical complexity, in Proc. 5th International Conference on Pattern Recognition, Miami Beach, 1980, 1324–1347.Google Scholar

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

Personalised recommendations