Complexity Results for Equistable Graphs and Related Classes
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equistable.pdf
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Author(s)
Milanic, Martin
Orlin, James B.
Rudolf, Gabor
Date Issued
January 2011
Journal
Annals of Operations Research
Publisher
Springer Science + Business Media B.V.
Citation
Milanič, Martin, James Orlin, and Gábor Rudolf. “Complexity Results for Equistable Graphs and Related Classes.” Annals of Operations Research 188.1 (2010): 359–370. CrossRef. Web.
Version
Author's final manuscript
Abstract
The class of equistable graphs is defined by the existence of a cost structure on the vertices such that the maximal stable sets are characterized by their costs. This graph class, not contained in any nontrivial hereditary class, has so far been studied mostly from a structural point of view; characterizations and polynomial time recognition algorithms have been obtained for special cases.
We focus on complexity issues for equistable graphs and related classes. We describe a simple pseudo-polynomial-time dynamic programming algorithm to solve the maximum weight stable set problem along with the weighted independent domination problem in some classes of graphs, including equistable graphs. Our results are obtained within the wider context of Boolean optimization; corresponding hardness results are also provided. More specifically, we show that the above problems are APX-hard for equistable graphs and that it is co-NP-complete to determine whether a given cost function on the vertices of a graph defines an equistable cost structure of that graph.
MIT Department
Sloan School of Management
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10479-010-0720-3
