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by Jerrum-sinclair Chain, V. S. Anil Kumar, H. Ramesh
http://drona.csa.iisc.ernet.in/~ramesh/psfiles/27.ps.gz
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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
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