Parameterized Algorithms for Stochastic Steiner Tree Problems

  • Denis Kurz
  • Petra Mutzel
  • Bernd Zey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7721)


We consider the Steiner tree problem in graphs under uncertainty, the so-called two-stage stochastic Steiner tree problem (SSTP). The problem consists of two stages: In the first stage, we do not know which nodes need to be connected. Instead, we know costs at which we may buy edges, and a set of possible scenarios one of which will arise in the second stage. Each scenario consists of its own terminal set, a probability, and second-stage edge costs. We want to find a selection of first-stage edges and second-stage edges for each scenario that minimizes the expected costs and satisfies all connectivity requirements. We show that SSTP is in the class of fixed-parameter tractable problems (FPT), parameterized by the number of terminals. Additionally, we transfer our results to the directed and the prize-collecting variant of SSTP.


Root Node Minimum Span Tree Steiner Tree Weighted Graph Steiner Tree Problem 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Denis Kurz
    • 1
  • Petra Mutzel
    • 1
  • Bernd Zey
    • 1
  1. 1.Department of Computer ScienceTU DortmundGermany

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