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Prize-Collecting Steiner Network Problems

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Integer Programming and Combinatorial Optimization (IPCO 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6080))

Abstract

In the Steiner Network problem we are given a graph G with edge-costs and connectivity requirements r uv between node pairs u,v. The goal is to find a minimum-cost subgraph H of G that contains r uv 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 r uv  ∈ {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.

Part of this work was done while the authors were meeting at DIMACS. We would like to thank DIMACS for hospitality.

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Author information

Authors and Affiliations

  1. AT&T Research Lab Research,  

    MohammadTaghi Hajiaghayi

  2. IBM T.J.Watson Research Center,  

    Rohit Khandekar

  3. Rutgers University, Camden,  

    Guy Kortsarz

  4. The Open University of Israel,  

    Zeev Nutov

Authors
  1. MohammadTaghi Hajiaghayi
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  2. Rohit Khandekar
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  3. Guy Kortsarz
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  4. Zeev Nutov
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, École Polytechnique Féderale de Lausanne, 1015, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. McGill University, 805 Sherbrooke West, H3A 2K6, Montreal, Quebec, Canada

    F. Bruce Shepherd

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Hajiaghayi, M., Khandekar, R., Kortsarz, G., Nutov, Z. (2010). Prize-Collecting Steiner Network Problems. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-13036-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13035-9

  • Online ISBN: 978-3-642-13036-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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