Parameterized Algorithms for Stochastic Steiner Tree Problems
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- Kurz D., Mutzel P., Zey B. (2013) Parameterized Algorithms for Stochastic Steiner Tree Problems. In: Kučera A., Henzinger T.A., Nešetřil J., Vojnar T., Antoš D. (eds) Mathematical and Engineering Methods in Computer Science. MEMICS 2012. Lecture Notes in Computer Science, vol 7721. Springer, Berlin, Heidelberg
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.
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