Stopping Times, Metrics and Approximate Counting

  • Magnus Bordewich
  • Martin Dyer
  • Marek Karpinski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


In this paper we examine the importance of the choice of metric in path coupling, and its relationship to stopping time analysis. We give strong evidence that stopping time analysis is no more powerful than standard path coupling. In particular, we prove a stronger theorem for path coupling with stopping times, using a metric which allows us to analyse a one-step path coupling. This approach provides insight for the design of better metrics for specific problems. We give illustrative applications to hypergraph independent sets and SAT instances, hypergraph colourings and colourings of bipartite graphs, obtaining improved results for all these problems.


Markov Chain Bipartite Graph Stopping Time Glauber Dynamic Proper Colouring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Magnus Bordewich
    • 1
  • Martin Dyer
    • 2
  • Marek Karpinski
    • 3
  1. 1.Durham UniversityDurhamUK
  2. 2.Leeds UniversityLeedsUK
  3. 3.University of BonnBonnGermany

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