Dyer, M orcid.org/0000-0002-2018-0374, Greenhill, C, Kleer, P et al. (2 more authors) (2021) Sampling hypergraphs with given degrees. Discrete Mathematics, 344 (11). 112566. ISSN 0012-365X
Abstract
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm , and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a positive constant.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Elsevier B.V. All rights reserved. This is an author produced version of an article, published in Discrete Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Hypergraph; Degree sequence; Sampling; Algorithm; Markov chain |
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: | 13 Oct 2021 12:03 |
Last Modified: | 17 Aug 2022 00:15 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.disc.2021.112566 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:179182 |