College of Computing, Georgia Institute of Technology, Atlanta, GA 30332.
Variable length path coupling†
Article first published online: 27 FEB 2007
Copyright © 2007 Wiley Periodicals, Inc.
Random Structures & Algorithms
Volume 31, Issue 3, pages 251–272, October 2007
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.
- 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
- NSF. Grant Number: (CCF-0455666)
- random sampling;
- Markov Chain Monte Carlo;
- path coupling;
- non-Markovian coupling
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