Very rapid mixing of the Glauber dynamics for proper colorings on bounded-degree graphs
Random Structures & Algorithms
ON THE CONVERGENCE OF METROPOLIS-TYPE RELAXATION AND ANNEALING WITH CONSTRAINTS
Probability in the Engineering and Informational Sciences
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed 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
Random Structures & Algorithms
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
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A new method for analyzing the mixing time of Markov chains is described. This method is an extension of path coupling and involves analyzing the coupling over multiple steps. The expected behavior of the coupling at a certain stopping time is used to bound the expected behavior of the coupling after a fixed number of steps. The new method is applied to analyze the mixing time of the Glauber dynamics for graph colorings. We show that the Glauber dynamics has O(n log(n)) mixing time for triangle-free $\Delta$-regular graphs if k colors are used, where $k\geq (2-\eta)\Delta$, for some small positive constant $\eta$. This is the first proof of an optimal upper bound for the mixing time of the Glauber dynamics for some values of k in the range $k\leq 2\Delta$.