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College of Computing, Georgia Institute of Technology, Atlanta, GA 30332.
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Variable length path coupling†
Article first published online: 27 FEB 2007
DOI: 10.1002/rsa.20166
Copyright © 2007 Wiley Periodicals, Inc.
Additional Information
How to Cite
Hayes, T. P. and Vigoda, E. (2007), Variable length path coupling. Random Struct. Alg., 31: 251–272. doi: 10.1002/rsa.20166
- †
A preliminary version of this paper appeared in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 2004, pp. 103–110.
- ‡
College of Computing, Georgia Institute of Technology, Atlanta, GA 30332.
Publication History
- Issue published online: 29 AUG 2007
- Article first published online: 27 FEB 2007
- Manuscript Accepted: 16 JUN 2006
- Manuscript Revised: 20 MAR 2006
- Manuscript Received: 9 JAN 2005
Funded by
- NSF. Grant Number: (CCF-0455666)
- Abstract
- References
- Cited By
Keywords:
- random sampling;
- Markov Chain Monte Carlo;
- path coupling;
- non-Markovian coupling
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 multistep (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. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007