Path Coupling Using Stopping Times and Counting Independent Sets and Colourings in Hypergraphs
Probability
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0501081,
title = {Path Coupling Using Stopping Times and Counting Independent Sets and Colourings in Hypergraphs},
author = {Magnus Bordewich and Martin Dyer and Marek Karpinski},
journal= {arXiv preprint arXiv:math/0501081},
year = {2007}
}
Comments
Simpler proof of main theorem. Improved bound on mixing time. 19 pages