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arXiv · 1705.10243

Directed random walks on polytopes with few facets

Malte Milatz
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Abstract

Let $P$ be a simple polytope with $n-d = 2$, where $d$ is the dimension and $n$ is the number of facets. The graph of such a polytope is also called a grid. It is known that the directed random walk along the edges of $P$ terminates after $O(\log^2 n)$ steps, if the edges are oriented in a (pseudo-)linear fashion. We prove that the same bound holds for the more general unique sink orientations.

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Malte Milatz. 2017-05-29. Directed random walks on polytopes with few facets. https://arxiv.org/abs/1705.10243

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