Path Coupling Using Stopping Times and Counting Independent Sets and Colourings in Hypergraphs

Magnus Bordewich; Martin Dyer; Marek Karpinski

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Path Coupling Using Stopping Times and Counting Independent Sets and Colourings in Hypergraphs

Magnus Bordewich·Martin Dyer·Marek Karpinski

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Abstract

We give a new method for analysing the mixing time of a Markov chain using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Delta of a vertex and the minimum size m of an edge satisfy m>= 2Delta+1. We also show that the Glauber dynamics for proper q-colourings of a hypergraph mixes rapidly if m>= 4 and q > Delta, and if m=3 and q>=1.65Delta. We give related results on the hardness of exact and approximate counting for both problems.

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BibTeX RIS

Magnus Bordewich, Martin Dyer, Marek Karpinski. 2005-04-02. Path Coupling Using Stopping Times and Counting Independent Sets and Colourings in Hypergraphs. https://arxiv.org/abs/math/0501081

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