An O(log n)-competitive algorithm for online constrained forest problems

Authors:
Jiawei Qian;David P. Williamson
Affiliations:
School of Operations Research and Information Engineering, Cornell University, Ithaca, NY;School of Operations Research and Information Engineering, Cornell University, Ithaca, NY
Venue:
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Year:
2011

Citing 6
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Abstract

In the generalized Steiner tree problem, we find a minimumcost 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(log n)-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(log n)-competitive algorithm for online constrained forest problems, including an online version of the prize-collecting Steiner tree problem.