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2000

Finding Small Triangulations of Polytope Boundaries Is Hard

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Finding Small Triangulations of Polytope Boundaries Is Hard
We prove that it is NP-hard to decide whether a polyhedral 3-ball can be triangulated with k simplices. The construction also implies that it is difficult to find the minimal triangulation of such a 3-ball. A lifting argument is used to transfer the result also to triangulations of boundaries of 4-polytopes. The proof is constructive and translates a variant of the 3-SAT problem into an instance of a concrete polyhedral 3-ball for which it is difficult to find a minimal triangulation.
Jürgen Richter-Gebert
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where DCG
Authors Jürgen Richter-Gebert
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