Dyer, ME, Jerrum, MR and Muller, H (2016) On the switch Markov chain for perfect matchings. In: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms. Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, 10-12 Jan 2016, Arlington, Virginia, USA. SIAM , pp. 1972-1983. ISBN 978-1-611974-12-6
Abstract
We study a simple Markov chain, the switch chain, on the set of all perfect matchings in a bipartite graph. This Markov chain was proposed by Diaconis, Graham and Holmes as a possible approach to a sampling problem arising in Statistics. They considered several classes of graphs, and conjectured that the switch chain would mix rapidly for graphs in these classes. Here we settle their conjecture almost completely. We ask: for which graph classes is the Markov chain ergodic and for which is it rapidly mixing? We provide a precise answer to the ergodicity question and close bounds on the mixing question. We show for the first time that the mixing time of the switch chain is polynomial in the class of monotone graphs. This class was identified by Diaconis, Graham and Holmes as being of particular interest in the statistical setting.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Martin Dyer, Mark Jerrum, Haiko Muller. This is an author produced version of a paper published in Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms. |
Dates: |
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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/M004953/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Feb 2016 13:13 |
Last Modified: | 11 Apr 2017 05:31 |
Published Version: | http://dx.doi.org/10.1137/1.9781611974331.ch138 |
Status: | Published |
Publisher: | SIAM |
Identification Number: | 10.1137/1.9781611974331.ch138 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94598 |