TY - GEN

T1 - Prize-collecting Steiner network problems

AU - Hajiaghayi, Mohammad Taghi

AU - Khandekar, Rohit

AU - Kortsarz, Guy

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2010

Y1 - 2010

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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=77954393830&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-13036-6_6

DO - 10.1007/978-3-642-13036-6_6

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AN - SCOPUS:77954393830

SN - 3642130356

SN - 9783642130359

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 71

EP - 84

BT - Integer Programming and Combinatorial Optimization - 14th International Conference, IPCO 2010, Proceedings

PB - Springer Verlag

T2 - 14th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2010

Y2 - 9 June 2010 through 11 June 2010

ER -