Dyer, M, Greenhill, C and Müller, H (2019) Counting independent sets in graphs with bounded bipartite pathwidth. In: Sau, I and Thilikos, D, (eds.) Graph-Theoretic concepts in computer science. Lecture Notes in Computer Science 11789. WG 2019, 19-21 Jun 2019, Vall de Nuria, Catalonia, Spain. Springer Verlag . ISBN 9783030307851
Abstract
The Glauber dynamics can efficiently sample independent sets almost uniformly at random in polynomial time for graphs in a certain class. The class is determined by boundedness of a new graph parameter called bipartite pathwidth. This result, which we prove for the more general hardcore distribution with fugacity λ, can be viewed as a strong generalisation of Jerrum and Sinclair’s work on approximately counting matchings. The class of graphs with bounded bipartite path-width includes line graphs and claw-free graphs, which generalise line graphs. We consider two further generalisations of claw-free graphs and prove that these classes have bounded bipartite pathwidth.
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2019. This is an author produced version of a paper published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | Markov chain Monte Carlo algorithm; Fully polynomial-time randomized approximation scheme; Independent set; Pathwidth | ||||
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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) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 17 Jul 2019 12:39 | ||||
Last Modified: | 12 Sep 2020 00:38 | ||||
Status: | Published | ||||
Publisher: | Springer Verlag | ||||
Identification Number: | https://doi.org/10.1007/978-3-030-30786-8_23 |