Hitting diamonds and growing cacti

Authors:
Samuel Fiorini;Gwenaël Joret;Ugo Pietropaoli
Affiliations:
Département de Mathématique, Université Libre de Bruxelles (ULB), Brussels, Belgium;Département d'Informatique, Université Libre de Bruxelles (ULB), Brussels, Belgium;Dipartimento di Ingegneria dell'Impresa, Università di Roma “Tor Vergata”, Rome, Italy
Venue:
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Year:
2010

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Abstract

We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primal-dual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is Θ(logn), where n denotes the number of vertices in the graph.