Stopping times, metrics and approximate counting

Bordewich, M.; Dyer, M.; Karpinski, M.

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.

Citation

Bordewich, M., Dyer, M., & Karpinski, M. (2006, July). Stopping times, metrics and approximate counting. Presented at 33rd International Colloquium of Automata, Languages and Programming (ICALP 2006)., Venice, Italy

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 33rd International Colloquium of Automata, Languages and Programming (ICALP 2006).
• Start Date: Jul 10, 2006
• End Date: Jul 12, 2006
• Publication Date: Jul 1, 2006
• Deposit Date: Oct 28, 2008
• Print ISSN: 0302-9743
• Pages: 108-119
• Series Title: Lecture notes in computer science
• Series Number: 4051
• Series ISSN: 0302-9743,1611-3349
• Book Title: Automata, languages and programming : 33rd International Colloquium, ICALP 2006, 10-14 July 2006, Venice, Italy ; proceedings, part I
• DOI: https://doi.org/10.1007/11786986_11
• Public URL: https://durham-repository.worktribe.com/output/1694562
• Publisher URL: http://dx.doi.org/10.1007/11786986_11