Abstract
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.
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Bordewich, M., Dyer, M., Karpinski, M. (2006). Stopping Times, Metrics and Approximate Counting. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_11
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DOI: https://doi.org/10.1007/11786986_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35904-3
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