Bordewich, M. and Dyer, M. and Karpinski, M. (2005) 'Path coupling using stopping times.', in Fundamentals of computation theory :15th International Symposium, FCT 2005, 17-20 August 2005, Lübeck, Germany ; proceedings. Berlin: Springer, pp. 19-31. Lecture notes in computer science. (3623).
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 $\Delta$ of a vertex and the minimum size $m$ of an edge satisfy $m\geq 2\Delta+1$. We also state results that the Glauber dynamics for proper $q$-colourings of a hypergraph mixes rapidly if $m\geq 4$ and $q > \Delta$, and if $m=3$ and $q\geq1.65\Delta$. We give related results on the hardness of exact and approximate counting for both problems.
|Item Type:||Book chapter|
|Keywords:||Hypergraph, Graph colouring, Independent set.|
|Full text:||Full text not available from this repository.|
|Publisher Web site:||http://dx.doi.org/10.1007/11537311|
|Record Created:||30 Oct 2008|
|Last Modified:||08 Nov 2010 12:22|
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