How hard is it to marry at random? (On the approximation of the permanent)
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On coupling and the approximation of the permanent
Information Processing Letters
SIAM Journal on Computing
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Convergence rates for Markov chains
SIAM Review
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Approximately counting up to four (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An elementary analysis of a procedure for sampling points in a convex body
Random Structures & Algorithms
Delayed path coupling and generating random permutations via distributed stochastic processes
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Faster random generation of linear extensions
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Markov chains and polynomial time algorithms
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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We show that no Markovian Coupling argument can prove rapid mixing of the Jerrum-Sinclair Markov chain for sampling almost uniformly from the set of perfect and near perfect matchings of a given graph. In particular, we show that there exists a bipartite graph G such that any Markovian coupling argument on the Jerrum-Sinclair Markov chain for G must necessarily take time exponential in the number of vertices in G.This holds even when the coupling argument is Time-Variant, i.e., the transition probabilities used by the coupling process depend upon the history of the process. In contrast, the above Markov chain on G has been shown to mix in polynomial time using conductance arguments.