Independent Set in P5-Free Graphs in Polynomial Time

Abstract

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2014 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Independent Set in P5-Free Graphs in Polynomial TimeDaniel Lokshantov, Martin Vatshelle, and Yngve VillangerDaniel LokshantovDepartment of Informatics, University of Bergen, Norway.Department of Informatics, University of Bergen, NorwayDepartment of Informatics, University of Bergen, Norway*Lokshtanov is supported by the Bergen Research Foundation, under the BeHard grant.Search for more papers by this author, Martin VatshelleDepartment of Informatics, University of Bergen, Norway.Department of Informatics, University of Bergen, NorwayDepartment of Informatics, University of Bergen, Norway*Lokshtanov is supported by the Bergen Research Foundation, under the BeHard grant.Search for more papers by this author, and Yngve VillangerDepartment of Informatics, University of Bergen, Norway.Department of Informatics, University of Bergen, NorwayDepartment of Informatics, University of Bergen, Norway*Lokshtanov is supported by the Bergen Research Foundation, under the BeHard grant.Search for more papers by this authorpp.570 - 581Chapter DOI:https://doi.org/10.1137/1.9781611973402.43PDFBibTexSections ToolsAdd to favoritesDownload CitationsTrack CitationsEmail SectionsAboutAbstract The Independent Set problem is NP-hard in general, however polynomial time algorithms exist for the problem on various specific graph classes. Over the last couple of decades there has been a long sequence of papers exploring the boundary between the NP-hard and polynomial time solvable cases. In particular the complexity of Independent Set on P5-free graphs has received significant attention, and there has been a long list of results showing that the problem becomes polynomial time solvable on sub-classes of P5-free graphs. In this paper we give the first polynomial time algorithm for Independent Set on P5-free graphs. Our algorithm also works for the Weighted Independent Set problem. Previous chapter Next chapter RelatedDetails Published:2014ISBN:978-1-61197-338-9eISBN:978-1-61197-340-2 https://doi.org/10.1137/1.9781611973402Book Series Name:ProceedingsBook Code:PRDA14Book Pages:viii + 1885