Graph orientations with no sink and an approximation for a hard case of #SAT
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Faster random generation of linear extensions
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast convergence of the Glauber dynamics for sampling independent sets
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
On Markov chains for independent sets
Journal of Algorithms
An Extension of Path Coupling and Its Application to the Glauber Dynamics for Graph Colorings
SIAM Journal on 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
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Randomly Coloring Constant Degree Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A very simple algorithm for estimating the number of k‐colorings of a low‐degree graph
Random Structures & Algorithms
Path coupling using stopping times
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Dobrushin conditions for systematic scan with block dynamics
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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In this paper we examine the importance of the choice of metric in path coupling, and its relationship to stopping time analysis. We give strong evidence that stopping time analysis is no more powerful than standard path coupling. In particular, we prove a stronger theorem for path coupling with stopping times, using a metric which allows us to analyse a one-step path coupling. This approach provides insight for the design of better metrics for specific problems. We give illustrative applications to hypergraph independent sets and SAT instances, hypergraph colourings and colourings of bipartite graphs, obtaining improved results for all these problems.