Dyer, M orcid.org/0000-0002-2018-0374, Greenhill, C and Müller, H orcid.org/0000-0002-1123-1774 (2021) Counting independent sets in graphs with bounded bipartite pathwidth. Random Structures & Algorithms, 59 (2). pp. 204-237. ISSN 1042-9832
Abstract
We show that a simple Markov chain, 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 urn:x-wiley:rsa:media:rsa21003:rsa21003-math-0001, can be viewed as a strong generalization of Jerrum and Sinclair's work on approximately counting matchings, that is, independent sets in line graphs. The class of graphs with bounded bipartite pathwidth includes claw-free graphs, which generalize line graphs. We consider two further generalizations of claw-free graphs and prove that these classes have bounded bipartite pathwidth. We also show how to extend all our results to polynomially bounded vertex weights.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Wiley Periodicals LLC. This is the peer reviewed version of the following article: Dyer, M , Greenhill, C and Müller, H (2021) Counting independent sets in graphs with bounded bipartite pathwidth. Random Structures & Algorithms, 59 (2). pp. 204-237. ISSN 1042-9832, which has been published in final form at https://doi.org/10.1002/rsa.21003. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. |
Keywords: | approximate counting; independent sets; pathwidth |
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) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/S016562/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 May 2021 14:56 |
Last Modified: | 27 Jul 2022 12:30 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1002/rsa.21003 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:174580 |