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)


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.


Competitive Ratio Dual Variable Online Algorithm Dual Solution Steiner Tree Problem 
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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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