Prize-collecting Steiner network problems

Mohammad Taghi Hajiaghayi, Rohit Khandekar, Guy Kortsarz, Zeev Nutov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 14th International Conference, IPCO 2010, Proceedings
PublisherSpringer Verlag
Number of pages14
ISBN (Print)3642130356, 9783642130359
StatePublished - 2010
Event14th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2010 - Lausanne, China
Duration: 9 Jun 201011 Jun 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6080 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2010


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