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Path Coupling Using Stopping Times and Counting Independent Sets and
Colourings in Hypergraphs
release_4sjn6ofyvbdbjf5cphysail6k4
by
Magnus Bordewich, Martin Dyer, Marek Karpinski
Released
as a article
.
2005
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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math/0501081v2
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