A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
An elementary analysis of a procedure for sampling points in a convex body
Random Structures & Algorithms
Balls and bins: a study in negative dependence
Random Structures & Algorithms
Delayed path coupling and generating random permutations
Proceedings of the ninth international conference on on Random structures and algorithms
Coupling vs. conductance for the Jerrum-Sinclair chain
Random Structures & Algorithms
An Extension of Path Coupling and Its Application to the Glauber Dynamics for Graph Colorings
SIAM Journal on Computing
Very rapid mixing of the Glauber dynamics for proper colorings on bounded-degree graphs
Random Structures & Algorithms
Randomly coloring graphs of girth at least five
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A Non-Markovian Coupling for Randomly Sampling Colorings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
The Glauber Dynamics on Colorings of a Graph with High Girth and Maximum Degree
SIAM Journal on Computing
A general lower bound for mixing of single-site dynamics on graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
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 A preliminary version of this paper appeared in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 2004, pp. 103–110.