An approximation algorithm to the k-Steiner forest problem

Authors:
Peng Zhang
Affiliations:
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate University of Chinese Academy of Sciences, Beijing, China
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Abstract

Given a graph G, an integer k, and demands set D = {(s1, t1), ..., (sl, tl)}, the k-Steiner Forest problem finds a forest in graph G to connect at least k demands in D such that the cost of the forest is minimized. This problem is proposed by Hajiaghayi and Jain in SODA'06. Thereafter, using Lagrangian relaxation technique, Segev et al. give the first approximation algorithm to this problem in ESA'06, with performance ratio O(min{n2/3,√l} log l). We give a new approximation algorithm to this problem with performance ratio O(min{n2/3,√l} log k) via greedy approach, improving the previously best known ratio in the literature.