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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, October 10, 2017, 12:15 pm

**Duration**: 30 minutes

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

**Speaker**: Malte Milatz

Given a polytope with directed edges, a *directed random walk* on the polytope moves from vertex to vertex, always moving along one of the outgoing edges chosen uniformly at random. (You can just think of the Random-Edge algorithm for linear programming.)

Let $d$ denote the dimension and $n$ the number of facets. The number $r = n-d$ is called the corank of the polytope. We show that a directed random walk may take $\Omega(\log^r n)$ steps when $r$ is fixed and the edges are directed according to a linear function.

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