Abstract
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 [1] give a 2-approximation algorithm for the offline problem; Berman and Coulston [3] give an O(logn)-competitive algorithm for the online problem. Goemans and Williamson [4] 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agrawal, A., Klein, P., Ravi, R.: When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM Journal on Computing 24, 440–456 (1995)
Awerbuch, B., Azar, Y., Bartal, Y.: On-line generalized Steiner problem. Theoretical Computer Science 324, 313–324 (2004)
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)
Goemans, M.X., Williamson, D.P.: A general approximation technique for constrained forest problems. SIAM Journal on Computing 24, 296–317 (1995)
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)
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)
Imase, M., Waxman, B.M.: Dynamic Steiner tree problem. SIAM Journal on Discrete Mathematics 4, 369–384 (1991)
Williamson, D.P., Goemans, M.X., Mihail, M., Vazirani, V.V.: A primal-dual approximation algorithm for generalized Steiner network problems. Combinatorica 15, 435–454 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Qian, J., Williamson, D.P. (2011). An O(logn)-Competitive Algorithm for Online Constrained Forest Problems. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-22006-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22005-0
Online ISBN: 978-3-642-22006-7
eBook Packages: Computer ScienceComputer Science (R0)