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Markovian Coupling vs. Conductance for the Jerrum-Sinclair Chain

Kumar, Anil VS and Ramesh, H (1999) Markovian Coupling vs. Conductance for the Jerrum-Sinclair Chain. In: 40th Annual Symposium on Foundations of Computer Science,1999, 17-19 October, New York, 241 -251.


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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.

Item Type: Conference Paper
Publisher: IEEE
Additional Information: Copyright 1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 18 Jan 2007
Last Modified: 19 Sep 2010 04:24
URI: http://eprints.iisc.ac.in/id/eprint/5771

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