Random sampling of 3-colorings in ℤ2

Authors:
Leslie Ann Goldberg;Russell Martin;Mike Paterson
Affiliations:
Department of Computer Science, University of Warwick, Coventry CV4 7AL, United Kingdom/ www.dcs.warwick.ac.uk//&sim/martin;Department of Computer Science, University of Warwick, Coventry CV4 7AL, United Kingdom/ www.dcs.warwick.ac.uk//&sim/martin;Department of Computer Science, University of Warwick, Coventry CV4 7AL, United Kingdom/ www.dcs.warwick.ac.uk//&sim/martin
Venue:
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Year:
2004

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Abstract

We consider the problem of uniformly sampling proper 3-colorings of an m × n rectangular region of ℤ2. We show that the single-site “Glauber-dynamics” Markov chain is rapidly mixing. Our result complements an earlier result of Luby, Randall, and Sinclair, which demonstrates rapid mixing when there is a fixed boundary (whose color cannot be changed). © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004This work was partially supported by the EPSRC Grant GR/R44560/01 “Analysing Markov-Chain Based Random Sampling Algorithms” and by the IST Programme of the EU under Contracts Numbers IST-1999-14186 (ALCOM-FT) and IST-1999-14036 (RAND-APX). Part of the work was done during a visit to the Isaac Newton Institute.