Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, December 15, 2015, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Emo Welzl

A triple of points in the plane forms an *embracing triangle* if the origin lies in its convex hull; correspondingly, d+1 points in d-space form an *embracing simplex* if their convex hull contains the origin. Via Gale duality, the set of embracing simplices of a set S of points is in correspondence to the facets of some simplicial polytope, assuming that S forms with the origin a set in general position.

We discuss the complexity of counting the number of embracing simplices in a set S, starting with a simple formula for embracing triangles. As a by-product we can count the number of facets of the convex hull of n points in general position in d-space orders of magnitude faster than the number of these facets, provided n-d is constant. (Joint work with Alexander Pilz and Manuel Wettstein)

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