Variable length path coupling

Authors:
Thomas P. Hayes;Eric Vigoda
Affiliations:
University of Chicago, Chicago, IL;University of Chicago, Chicago, IL
Venue:
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2004

Citing 13
Cited 5

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
The Glauber dynamics on colourings of a graph with high girth and maximum degree

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
Improved Bounds for Sampling Coloring

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Markovian Coupling vs. Conductance for the Jerrum-Sinclair Chain

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Randomly Colouring Graphs with Lower Bounds on Girth and Maximum Degree

FOCS '01 Proceedings of the 42nd IEEE 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

Brief announcement: coupling for Markov decision processes - application to self-stabilization with arbitrary schedulers

Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Path coupling using stopping times and counting independent sets and colorings in hypergraphs

Random Structures & Algorithms
Stopping times, metrics and approximate counting

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Path coupling using stopping times

FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Randomly colouring graphs with girth five and large maximum degree

LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

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.