Abrishami, T., Chudnovsky, M., Dibek, C. et al. (1 more author) (2024) Submodular Functions and Perfect Graphs. Mathematics of Operations Research. ISSN 0364-765X
Abstract
We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph. An even pair in a graph is a pair of vertices all induced paths between which are even. An even set is a set of vertices every two of which are an even pair. We show that every perfect graph that does not contain a prism or a hole of length four as an induced subgraph has a balanced separator which is the union of a bounded number of even sets, where the bound depends only on the maximum degree of the graph. This allows us to solve the maximum weight independent set problem using the well-known submodular function minimization algorithm.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024, INFORMS. This is an author produced version of an article published in Mathematics of Operations Research. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Primary: 05C17, Secondary: 05C69, 05C85, 90C27, perfect graphs, submodular functions, maximum weight independent set, even sets |
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/V002813/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 Feb 2024 10:06 |
Last Modified: | 28 Feb 2024 16:36 |
Status: | Published online |
Publisher: | INFORMS |
Identification Number: | 10.1287/moor.2021.0302 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:209670 |