Complexity of Some Geometric and Topological Problems

  • Marcus Schaefer
Conference paper

DOI: 10.1007/978-3-642-11805-0_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)
Cite this paper as:
Schaefer M. (2010) Complexity of Some Geometric and Topological Problems. In: Eppstein D., Gansner E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg

Abstract

We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on the rectilinear crossing number and intersection graphs of line segments, we argue that there is a need to recognize this level of complexity as its own class.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marcus Schaefer
    • 1
  1. 1.DePaul UniversityChicagoUSA

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