Coupling vs. conductance for the Jerrum-Sinclair chain

Kumar, Anil VS and Ramesh, H (2001) Coupling vs. conductance for the Jerrum-Sinclair chain. In: Random Structures and Algorithms, 18 (1). pp. 1-17.

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Abstract

We address the following question: is the causal coupling method as strong as the conductance method in showing rapid mixing of Markov chains? A causal coupling is a coupling which uses only past and present information, but not information about the future. We answer the above question in the negative by showing that there exists a bipartite graph G such that any causal coupling argument on the Jerrum–Sinclair Markov chain for sampling almost uniformly from the set of perfect and near perfect matchings of G must necessarily take time exponential in the number of vertices in G. In contrast, the above Markov chain on G has been shown to mix in polynomial time using conductance arguments.

Item Type:	Journal Article
Publication:	Random Structures and Algorithms
Publisher:	Wiley Interscience
Additional Information:	Copyright of this article belongs to John Wiley & Sons
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	26 Dec 2008 10:49
Last Modified:	19 Sep 2010 04:53
URI:	http://eprints.iisc.ac.in/id/eprint/16692

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