Metric Construction, Stopping Times and Path Coupling
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.
Keywords
Cite
@article{arxiv.math/0511202,
title = {Metric Construction, Stopping Times and Path Coupling},
author = {Magnus Bordewich and Martin Dyer and Marek Karpinski},
journal= {arXiv preprint arXiv:math/0511202},
year = {2007}
}
Comments
21 pages, revised version includes statement and proof of general stopping times theorem (section 2.2), and additonal remarks in section 6