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An O(logn)-Competitive Algorithm for Online Constrained Forest Problems

  • Jiawei Qian
  • David P. Williamson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

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.

Keywords

Competitive Ratio Dual Variable Online Algorithm Dual Solution Steiner Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jiawei Qian
    • 1
  • David P. Williamson
    • 1
  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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