An O(logn)-Competitive Algorithm for Online Constrained Forest Problems
In the generalized Steiner tree problem, we find a minimum-cost set of edges to connect a given set of source-sink pairs. In the online version of this problem, the source-sink pairs arrive over time. Agrawal, Klein, and Ravi  give a 2-approximation algorithm for the offline problem; Berman and Coulston  give an O(logn)-competitive algorithm for the online problem. Goemans and Williamson  subsequently generalized the offline algorithm of Agrawal et al. to handle a large class of problems they called constrained forest problems, and other problems, such as the prize-collecting Steiner tree problem. In this paper, we show how to combine the ideas of Goemans and Williamson and those of Berman and Coulston to give an O(logn)-competitive algorithm for online constrained forest problems, including an online version of the prize-collecting Steiner tree problem.
KeywordsCompetitive Ratio Dual Variable Online Algorithm Dual Solution Steiner Tree Problem
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