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Path coupling using stopping times and counting independent sets and colourings in hypergraphs.

Bordewich, M. and Karpinski, M. and Dyer, M. (2008) 'Path coupling using stopping times and counting independent sets and colourings in hypergraphs.', Random structures and algorithms., 32 (3). pp. 375-399.

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 ∆ of a vertex and the minimum size m of an edge satisfy m ≥ 2 ∆ + 1. We also show that the Glauber dynamics for proper q-colorings of a hypergraph mixes rapidly if m ≥ 4 and q > ∆, and if m = 3 and q ≥ 1.65 ∆. We give related results on the hardness of exact and approximate counting for both problems.

Item Type:Article
Keywords:Path coupling, Markov chain Monte Carlo, Hypergraph coloring, Hypergraph independent set.
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1002/rsa.20204
Record Created:21 Dec 2009 15:35
Last Modified:06 Jan 2010 12:08

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