TY - JOUR

T1 - Prize-collecting steiner network problems

AU - Hajiaghayi, Mohammadtaghi

AU - Khandekar, Rohit

AU - Kortsarz, Guy

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2012/12

Y1 - 2012/12

N2 - 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 article, 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 nondecreasing 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 by Nagarajan et al. [2008]. We further generalize our results for element-connectivity and node-connectivity.

AB - 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 article, 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 nondecreasing 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 by Nagarajan et al. [2008]. We further generalize our results for element-connectivity and node-connectivity.

UR - http://www.scopus.com/inward/record.url?scp=84872480216&partnerID=8YFLogxK

U2 - 10.1145/2390176.2390178

DO - 10.1145/2390176.2390178

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AN - SCOPUS:84872480216

SN - 1549-6325

VL - 9

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 1

M1 - 2

ER -