Complexity of Some Geometric and Topological Problems

  • Marcus Schaefer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)


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.


Intersection Graph Existential Theory Constraint Network Topological Problem Universality Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marcus Schaefer
    • 1
  1. 1.DePaul UniversityChicagoUSA

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