Parameterized Algorithms for Stochastic Steiner Tree Problems

Since 1971, numerous parameterized algorithms for the Steiner tree problem have been published, first of which was introduced by Dreyfus and Wagner. However, up to today there is not a single parameterized algorithm for the two-stage stochastic Steiner tree problem. This problem is still practically important and deserves more attention. This document first presents an algorithm that has a worst-case running time of O((Kn)23t), where K is the number of scenarios, n is the number of vertices of the input graph and t∗ is the total number of terminals. Therefore, it places the two-stage stochastic Steiner tree problem as well as its prize-collecting variant in the complexity class FPT. Afterwards, a framework and some possible implementations are presented that might be suitable to parameterize the problem with the number of non-terminals.