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Prize-Collecting Steiner Network Problems

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by MohammadTaghi Hajiaghayi , Rohit Khandekar , Guy Kortsarz , Zeev Nutov
Citations:7 - 5 self
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BibTeX

@MISC{Hajiaghayi_prize-collectingsteiner,
    author = {MohammadTaghi Hajiaghayi and Rohit Khandekar and Guy Kortsarz and Zeev Nutov},
    title = {Prize-Collecting Steiner Network Problems},
    year = {}
}

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Abstract

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.

Keyphrases

prize-collecting steiner network problem    connectivity requirement    node pair    penalty function    classic prize-collecting steiner forest problem    ruv edge-disjoint path    novel linear programming relaxation    all-or-nothing penalty function    steiner network problem    open question    minimum-cost subgraph    first constant-factor approximation algorithm    monotone non-decreasing penalty function   

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