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.
Unable to display preview. Download preview PDF.
- 3.Berman, P., Coulston, C.: On-line algorithms for Steiner tree problems. In: Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, pp. 344–353 (1997)Google Scholar
- 5.Goemans, M., Goldberg, A., Plotkin, S., Shmoys, D., Tardos, E., Williamson, D.: Improved approximation algorithms for network design problems. In: Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 223–232 (1994)Google Scholar
- 6.Gupta, A., Krishnaswamy, R., Ravi, R.: Online and stochastic survivable network design. In: Proceedings of the 41st Annual ACM Symposium on the Theory of Computing, pp. 685–694 (2009)Google Scholar