Metric Construction, Stopping Times and Path Coupling

Magnus Bordewich; Martin Dyer; Marek Karpinski

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Metric Construction, Stopping Times and Path Coupling

Magnus Bordewich·Martin Dyer·Marek Karpinski

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Abstract

In this paper we examine the importance of the choice of metric in path coupling, and the relationship of this to \emph{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 restrict analysis to standard one-step path coupling. This approach provides insight for the design of non-standard metrics giving improvements in the analysis of specific problems. We give illustrative applications to hypergraph independent sets and SAT instances, hypergraph colourings and colourings of bipartite graphs.

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Magnus Bordewich, Martin Dyer, Marek Karpinski. 2005-11-22. Metric Construction, Stopping Times and Path Coupling. https://arxiv.org/abs/math/0511202

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