## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

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

Duration: 30 minutes

Location: CAB G51

Speaker: Malte Milatz

## Random walks on polytopes

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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