Finding Independent Sets in Unions of Perfect Graphs

Chakaravarthy, Venkatesan T.; Pandit, Vinayaka; Roy, Sambuddha; Sabharwal, Yogish

doi:10.4230/LIPIcs.FSTTCS.2010.251

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Finding Independent Sets in Unions of Perfect Graphs

Authors Venkatesan T. Chakaravarthy, Vinayaka Pandit, Sambuddha Roy, Yogish Sabharwal

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2010-12-14

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Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2010.251
URN: urn:nbn:de:0030-drops-28683

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Keywords

Approximation Algorithms; Comparability Graphs; Hardness of approximation

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Abstract

The maximum independent set problem (MaxIS) on general graphs is known to be NP-hard to approximate within a factor of $n^{1-epsilon}$, for any $epsilon > 0$. However, there are many ``easy" classes of graphs on which the problem can be solved in polynomial time. In this context, an interesting question is that of computing the maximum independent set in a graph that can be expressed as the union of a small number of graphs from an easy class. The MaxIS problem has been studied on unions of interval graphs and chordal graphs. We study the MaxIS problem on unions of perfect graphs (which generalize the above two classes). We present an $O(sqrt{n})$-approximation algorithm when the input graph is the 
union of two perfect graphs. We also show that the MaxIS problem on unions of two comparability graphs (a subclass of perfect graphs)
cannot be approximated within any constant factor.

Cite As Get BibTex

Venkatesan T. Chakaravarthy, Vinayaka Pandit, Sambuddha Roy, and Yogish Sabharwal. Finding Independent Sets in Unions of Perfect Graphs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 251-259, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010) https://doi.org/10.4230/LIPIcs.FSTTCS.2010.251

Author Details

Venkatesan T. Chakaravarthy

Vinayaka Pandit

Sambuddha Roy

Yogish Sabharwal

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