In the Steiner Network problem we are given a graph G with edge-costs and connectivity requirements ruv between node pairs u,v. The goal is to find a minimum-cost subgraph H of G that contains ruv edge-disjoint paths for all u,v ∈ V. In Prize-Collecting Steiner Network problems we do not need to satisfy all requirements, but are given a penalty function for violating the connectivity requirements, and the goal is to find a subgraph H that minimizes the cost plus the penalty. The case when ruv ∈ {0,1} is the classic Prize-Collecting Steiner Forest problem. In this paper we present a novel linear programming relaxation for the Prize-Collecting Steiner Network problem, and by rounding it, obtain the first constant-factor approximation algorithm for submodular and monotone non-decreasing penalty functions. In particular, our setting includes all-or-nothing penalty functions, which charge the penalty even if the connectivity requirement is slightly violated; this resolves an open question posed in [SSW07]. We further generalize our results for element-connectivity and node-connectivity. © 2010 Springer-Verlag.
CITATION STYLE
Hajiaghayi, M. T., Khandekar, R., Kortsarz, G., & Nutov, Z. (2010). Prize-collecting Steiner network problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6080 LNCS, pp. 71–84). Springer Verlag. https://doi.org/10.1007/978-3-642-13036-6_6
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