Hitting Diamonds and Growing Cacti

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Authors
Fiorini, Samuel
Joret, Gwenaël
Pietropaoli, Ugo
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Abstract
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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.
Comment: v2: several minor changes.
Keywords
Computer Science - Data Structures and Algorithms, Computer Science - Discrete Mathematics
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