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.
This work was supported by the “Actions de Recherche Concertées” (ARC) fund of the “Communauté française de Belgique”.
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Fiorini, S., Joret, G., Pietropaoli, U. (2010). Hitting Diamonds and Growing Cacti. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_15
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DOI: https://doi.org/10.1007/978-3-642-13036-6_15
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