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On the conductance of order Markov chains

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Abstract

Let Q be a convex solid in ℝn, partitioned into two volumes u and v by an area s. We show that s>min(u,v)/diam Q, and use this inequality to obtain the lower bound n -5/2 on the conductance of order Markov chains, which describe nearly uniform generators of linear extensions for posets of size n. We also discuss an application of the above results to the problem of sorting of posets.

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Authors and Affiliations

  1. Institute for Systems Studies of the U.S.S.R. Academy of Sciences, U.S.S.R.

    Alexander Karzanov

  2. Department of Computer Science, Rutgers University, 08903, New Brunswick, NJ, U.S.A.

    Leonid Khachiyan

Authors
  1. Alexander Karzanov
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  2. Leonid Khachiyan
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Communicated by I. Rival

Computing Center of the USSR Academy of Sciences USSR

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Karzanov, A., Khachiyan, L. On the conductance of order Markov chains. Order 8, 7–15 (1991). https://doi.org/10.1007/BF00385809

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  • DOI: https://doi.org/10.1007/BF00385809

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