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Hitting Diamonds and Growing Cacti (0911.4366v2)
Published 23 Nov 2009 in cs.DS and cs.DM
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 \Theta(\log n), where n denotes the number of vertices in the graph.