A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
A more rapidly mixing Markov chain for graph colorings
proceedings of the eighth international conference on Random structures and algorithms
On Markov chains for independent sets
Journal of Algorithms
Randomized algorithms: approximation, generation, and counting
Randomized algorithms: approximation, generation, and counting
Markov Chain Algorithms for Planar Lattice Structures
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
Random sampling of 3-colorings in ℤ2
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Sampling Eulerian orientations of triangular lattice graphs
Journal of Discrete Algorithms
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Path coupling is a useful technique for simplifying the analysis of a coupling of a Markov chain. Rather than defining and analysing the coupling on every pair in @Wx@W, where @W is the state space of the Markov chain, analysis is done on a smaller set S@?@Wx@W. If the coefficient of contraction @b is strictly less than one, no further analysis is needed in order to show rapid mixing. However, if @b=1 then analysis (of the variance) is still required for all pairs in @Wx@W. In this paper we present a new approach which shows rapid mixing in the case @b=1 with a further condition which only needs to be checked for pairs in S, greatly simplifying the work involved. We also present a technique applicable when @b=1 and our condition is not met.