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.
In text/plain format

Archived Files and Locations

application/pdf  278.7 kB
file_5iiujdi26ncvrpowttpavfxu4m
archive.org (archive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2005-04-02
Version   v2
Language   en ?
arXiv  math/0501081v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 91973ca7-449d-4c97-87b4-644d68b93fe2
API URL: JSON