The complexity of finding small triangulations of convex 3-polytopes

Authors:
Alexander Below;Jesús A. De Loera;Jürgen Richter-Gebert
Affiliations:
Institut für Theoretische Informatik, ETH-Zürich, Switzerland;Department of Mathematics, University of California, Davis, CA;Technische Universität München, Zentrum Mathematik and Institut für Theoretische Informatik, ETH-Zürich, Switzerland
Venue:
Journal of Algorithms - Special issue: SODA 2000
Year:
2004

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Abstract

We present a polynomial transformation from the satisfiability problem to the problem of finding a triangulation of a convex 3-polytope that uses a small number of tetrahedra. We also discuss other complexity results related to optimal triangulations.