Article

Variable length path coupling

Authors:

Thomas P. Hayes and

Eric VigodaAuthors Info & Claims

SODA '04: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms

January 2004

Pages 103 - 110

Published: 11 January 2004 Publication History

Abstract

We present a new technique for constructing and analyzing couplings to bound the convergence rate of finite Markov chains. Our main theorem is a generalization of the path coupling theorem of Bubley and Dyer, allowing the defining partial couplings to have length determined by a random stopping time. Unlike the original path coupling theorem, our version can produce multi-step (non-Markovian) couplings. Using our variable length path coupling theorem, we improve the upper bound on the mixing time of the Glauber dynamics for randomly sampling colorings.

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T. P. Hayes and E. Vigoda. A non-Markovian coupling for randomly sampling colorings. To appear in 44th Annual Symposium on Foundations of Computer Science, 2003.

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Cited By

Bordewich MDyer MKarpinski M(2006)Stopping times, metrics and approximate countingProceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I10.1007/11786986_11(108-119)Online publication date: 10-Jul-2006
https://dl.acm.org/doi/10.1007/11786986_11
Lau LMolloy M(2006)Randomly colouring graphs with girth five and large maximum degreeProceedings of the 7th Latin American conference on Theoretical Informatics10.1007/11682462_61(665-676)Online publication date: 20-Mar-2006
https://dl.acm.org/doi/10.1007/11682462_61
Fribourg LMessika SAguilera MAspnes J(2005)Brief announcementProceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing10.1145/1073814.1073875(322-322)Online publication date: 17-Jul-2005
https://dl.acm.org/doi/10.1145/1073814.1073875
Show More Cited By

Variable length path coupling
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic representations
    2. Stochastic processes
2. Theory of computation

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Published In

cover image ACM Conferences

SODA '04: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms

January 2004

1113 pages

ISBN:089871558X

Program Chair:
Ian Munro

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Society for Industrial and Applied Mathematics

United States

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Published: 11 January 2004

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Bordewich MDyer MKarpinski M(2006)Stopping times, metrics and approximate countingProceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I10.1007/11786986_11(108-119)Online publication date: 10-Jul-2006
https://dl.acm.org/doi/10.1007/11786986_11
Lau LMolloy M(2006)Randomly colouring graphs with girth five and large maximum degreeProceedings of the 7th Latin American conference on Theoretical Informatics10.1007/11682462_61(665-676)Online publication date: 20-Mar-2006
https://dl.acm.org/doi/10.1007/11682462_61
Fribourg LMessika SAguilera MAspnes J(2005)Brief announcementProceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing10.1145/1073814.1073875(322-322)Online publication date: 17-Jul-2005
https://dl.acm.org/doi/10.1145/1073814.1073875
Bordewich MDyer MKarpinski M(2005)Path coupling using stopping timesProceedings of the 15th international conference on Fundamentals of Computation Theory10.1007/11537311_3(19-31)Online publication date: 17-Aug-2005
https://dl.acm.org/doi/10.1007/11537311_3

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