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Path Coupling Using Stopping Times

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Fundamentals of Computation Theory (FCT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3623))

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Abstract

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ +1. We also state results that the Glauber dynamics for proper q-colourings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥1.65Δ. We give related results on the hardness of exact and approximate counting for both problems.

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References

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Author information

Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, LS2 9JT, UK

    Magnus Bordewich & Martin Dyer

  2. Dept. of Computer Science, University of Bonn, 53117, Bonn, Germany

    Marek Karpinski

Authors
  1. Magnus Bordewich
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  2. Martin Dyer
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  3. Marek Karpinski
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Informatik, Universität zu Lübeck, Germany

    Maciej Liśkiewicz

  2. Institut für Theoretische Informatik, Universität zu Lübeck, Ratzeburger Allee 160, 23538, Lübeck, Germany

    Rüdiger Reischuk

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© 2005 Springer-Verlag Berlin Heidelberg

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Bordewich, M., Dyer, M., Karpinski, M. (2005). Path Coupling Using Stopping Times. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_3

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  • DOI: https://doi.org/10.1007/11537311_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28193-1

  • Online ISBN: 978-3-540-31873-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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