Weighted Coloring: further complexity and approximability results

Authors:
Bruno Escoffier;Jérôme Monnot;Vangelis Th. Paschos
Affiliations:
LAMSADE, CNRS and Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;LAMSADE, CNRS and Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;LAMSADE, CNRS and Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Venue:
Information Processing Letters
Year:
2006

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Abstract

Given a vertex-weighted graph G=(V,E;w), w(v)=0 for any v@?V, we consider a weighted version of the coloring problem which consists in finding a partition S=(S"1,...,S"k) of the vertex set of G into stable sets and minimizing @?"i"="1^kw(S"i) where the weight of S is defined as max{w(v):v@?S}. In this paper, we continue the investigation of the complexity and the approximability of this problem by answering some of the questions raised by Guan and Zhu [D.J. Guan, X. Zhu, A coloring problem for weighted graphs, Inform. Process. Lett. 61 (2) (1997) 77-81].