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Stopping times, metrics and approximate counting.

Bordewich, M. and Dyer, M. and Karpinski, M. (2006) 'Stopping times, metrics and approximate counting.', in Automata, languages and programming : 33rd International Colloquium, ICALP 2006, 10-14 July 2006, Venice, Italy ; proceedings, part I. Berlin: Springer, pp. 108-119. Lecture notes in computer science. (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.

Item Type:Book chapter
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Date of first online publication:July 2006
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