Computing optimal triangulations of convex polytopes

by Jesus de Loera

Abstract:

We examine the difficulty of the problem: Given a convex d-polytope find a triangulation that uses K d-simplices. In the second part of the talk we discuss a polyhedral optimization approach to obtain explicit answers. We will present concrete experimental results (in particular the triangulations with minimal/maximal number of simplices for several famous polyhedra) as well an application to counting real roots of polynomials systems.

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