Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

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

Duration: 30 minutes

Location: OAT S15/S16/S17

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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