Efficient algorithms for the weighted 2-center problem in a cactus graph

Authors:
Boaz Ben-Moshe;Binay Bhattacharya;Qiaosheng Shi
Affiliations:
School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada;School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada;School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

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Abstract

In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n logn) time algorithm is proposed that finds the weighted 1-center in a cactus graph, where n is the number of vertices in the graph. For the weighted 2-center problem, an O(n log3n) time algorithm is devised for its continuous version and showed that its discrete version is solvable in O(n log2n) time. No such algorithm was previously known. The obnoxious center problem in a cactus graph can now be solved in O(n log3n). This improves the previous result of O(cn) where c is the number of distinct vertex weights used in the graph [8]. In the worst case c is O(n).