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Title: Approximate association via dissociation
Authors: You, J
Wang, JX
Cao, YX 
Keywords: Association set (cluster vertex deletion)
Dissociation set
Cluster graph
Modular decomposition
Triangle-free graph
Issue Date: 2017
Publisher: North-Holland
Source: Discrete applied mathematics, 11 Mar. 2017, v. 219, p. 202-209 How to cite?
Journal: Discrete applied mathematics 
Abstract: A vertex set X of a graph G is an association set if each component of G - X is a clique, and a dissociation set if each of these cliques has only one or two vertices. We observe some special structures and show that if none of them exists, then the minimum association set problem can be reduced to the minimum weighted dissociation set problem. This yields the first nontrivial approximation algorithm for the association set problem, with approximation ratio 2.5. The reduction is based on a combinatorial study of modular decomposition of graphs free of these special structures. Further, a novel algorithmic use of modular decomposition enables us to implement our algorithm in O(mn + n(2)) time.
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.11.007
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