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Prize-Collecting Steiner Network Problems

  • MohammadTaghi Hajiaghayi
  • Rohit Khandekar
  • Guy Kortsarz
  • Zeev Nutov
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Approximation Algorithm Penalty Function Steiner Tree Node Pair Network Design Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • MohammadTaghi Hajiaghayi
    • 1
  • Rohit Khandekar
    • 2
  • Guy Kortsarz
    • 3
  • Zeev Nutov
    • 4
  1. 1.AT&T Research Lab Research 
  2. 2.IBM T.J.Watson Research Center 
  3. 3.Rutgers University, Camden 
  4. 4.The Open University of Israel 

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