Stochastic Steiner Tree with Non-uniform Inflation

We study the Steiner Tree problem in the model of two-stage stochastic optimization with non-uniform inflation factors, and give a poly-logarithmic approximation factor for this problem. In this problem, we are given a graph G = (V, E), with each edge having two costs cM and cT (the costs for Monday and Tuesday, respectively). We are also given a probability distribution : 2V [0, 1] over subsets of V , and will be given a client set S drawn from this distribution on Tuesday. The algorithm has to buy a set of edges EM on Monday, and after the client set S is revealed on Tuesday, it has to buy a (possibly empty) set of edges ET (S) so that the edges in EM ET (S) connect all the nodes in S. The goal is to minimize the cM (EM ) + ES[ cT ( ET (S) ) ]. We give the first poly-logarithmic approximation algorithm for this problem. Our algorithm builds on the recent techniques developed by Chekuri et al. (FOCS 2006) for multi-commodity Cost-Distance. Previously, the problem had been studied fo...

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Anupam Gupta, MohammadTaghi Hajiaghayi, Amit Kumar
• Keywords: Algorithms, APPROX 2007, Poly-logarithmic Approximation, Steiner Tree Problem, Tuesday's Costs