Counting Polygon Triangulations is Hard

Author David Eppstein

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David Eppstein
  • Computer Science Department, University of California, Irvine, USA

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David Eppstein. Counting Polygon Triangulations is Hard. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We prove that it is #P-complete to count the triangulations of a (non-simple) polygon.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Problems, reductions and completeness
  • counting complexity
  • #P-completeness
  • triangulation
  • polygons


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