Path coupling using stopping times

Authors:
Magnus Bordewich;Martin Dyer;Marek Karpinski
Affiliations:
School of Computing, University of Leeds, Leeds, UK;School of Computing, University of Leeds, Leeds, UK;Dept. of Computer Science, University of Bonn, Bonn, Germany
Venue:
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Year:
2005

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Abstract

We analyse the mixing time of Markov chains 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 Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ +1. We also state results that the Glauber dynamics for proper q-colourings of a hypergraph mixes rapidly if m ≥ 4 and q Δ, and if m = 3 and q ≥1.65Δ. We give related results on the hardness of exact and approximate counting for both problems.