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LP approaches to improved approximation for clique transversal in perfect graphs
Authors
Samuel Fiorini
R. Krithika
N.S. N.S. Narayanaswamy
Venkatesh Raman
Publication date
1 January 2014
Publisher
'Springer Science and Business Media LLC'
Doi
Abstract
Given an undirected simple graph G, a subset T of vertices is an r-clique transversal if it has at least one vertex from every r-clique in G. I.e. T is an r-clique transversal if G-S is K r -free. r-clique transversals generalize vertex covers as a vertex cover is a set of vertices whose deletion results in a graph that is K 2-free. Perfect graphs are a well-studied class of graphs on which a minimum vertex cover can be obtained in polynomial time. However, the problem of finding a minimum r-clique transversal is NP-hard even for r=3. As any induced odd length cycle in a perfect graph is a triangle, a triangle-free perfect graph is bipartite. I.e. in perfect graphs, a 3-clique transversal is an odd cycle transversal. In this work, we describe an(r+1/2) -approximation algorithm for r-clique transversal on weighted perfect graphs improving on the straightforward r-approximation algorithm. We then show that 3-Clique Transversal is APX-hard on perfect graphs and it is NP-hard to approximate it within any constant factor better than 4/3 assuming the unique games conjecture. We also show intractability results in the parameterized complexity framework. © 2014 Springer-Verlag Berlin Heidelberg.SCOPUS: cp.kSCOPUS: cp.kinfo:eu-repo/semantics/publishe
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info:doi/10.1007%2F978-3-662-4...
Last time updated on 22/07/2021
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Last time updated on 23/02/2017