d-Transversals of stable sets and vertex covers in weighted bipartite graphs

Authors:
C. Bentz;M. -C. Costa;C. Picouleau;B. Ries;D. De Werra
Affiliations:
Université Paris-Sud, LRI, Orsay, France;ENSTA Paris-Tech and CEDRIC, Paris, France;CNAM, CEDRIC, Paris, France;Université Paris-Dauphine, LAMSADE, Paris, France;Ecole Polytechnique Fédérale de Lausanne EPFL, Switzerland
Venue:
Journal of Discrete Algorithms
Year:
2012

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Abstract

Let G=(V,E) be a graph in which every vertex v@?V has a weight w(v)=0 and a cost c(v)=0. Let S"G be the family of all maximum-weight stable sets in G. For any integer d=0, a minimum d-transversal in the graph G with respect to S"G is a subset of vertices T@?V of minimum total cost such that |T@?S|=d for every S@?S"G. In this paper, we present a polynomial-time algorithm to determine minimum d-transversals in bipartite graphs. Our algorithm is based on a characterization of maximum-weight stable sets in bipartite graphs. We also derive results on minimum d-transversals of minimum-weight vertex covers in weighted bipartite graphs.