Rheinische Friedrich-Wilhelms-Universität Bonn Institut für Informatik
 
Abteilung V

 
Universität Bonn -> Institut für Informatik -> Abteilung V
CS-Reports 2005 Copyright 2005 Universität Bonn, Institut für Informatik, Abt. V
85262

10.01.2005

Path Coupling Using Stopping Times and Counting Independent Sets and Colourings in Hypergraphs
Magnus Bordewich, Martin Dyer and Marek Karpinski
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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 Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show 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.

Last Change: 11/05/14 at 10:33:34
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Universität Bonn -> Institut für Informatik -> Abteilung V

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