Dyer, ME and Muller, H (2015) Graph classes and the switch Markov chain for matchings. Annales de la Faculte des Sciences de Toulouse, 24 (4). pp. 885-993. ISSN 0240-2963
Abstract
Diaconis, Graham and Holmes [8] studied the statistical applications of counting and sampling perfect matchings in certain classes of graphs. They proposed a simple Markov chain, called the switch chain here, to generate a matching almost uniformly at random for graphs in these classes. We examine these graph classes in detail, and show that they have a strong graph-theoretic rationale. We consider the ergodicity of the switch chain, and show that all the classes in [8] inherit their ergodicity from a larger class. We also study the computational complexity of the mixing time of the switch chain, and show that this has already been resolved for all but one of the classes in [8], that which Diaconis, Graham and Holmes called monotone graphs. We outline an approach to showing polynomial time convergence of the switch chain for monotone graphs. This is shown to rely upon an interesting, though unproven, conjecture concerning Hamilton cycles in monotone graphs.
Metadata
Item Type: | Article |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/I012087/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Feb 2016 12:10 |
Last Modified: | 22 Mar 2016 14:10 |
Published Version: | http://dx.doi.org/10.5802/afst.1469 |
Status: | Published |
Publisher: | Universite Paul Sabatier |
Identification Number: | 10.5802/afst.1469 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:95655 |