Improved algorithms for the minmax-regret 1-center problem

Authors:
Tzu-Chin Lin;Hung-I Yu;Biing-Feng Wang
Affiliations:
Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, Republic of China;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, Republic of China;Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, Republic of China
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

This paper studies the problem of finding the 1-center on a graph where vertex weights are uncertain and the uncertainty is characterized by given intervals. It is required to find a minmax-regret solution, which minimizes the worst-case loss in the objective function. Averbakh and Berman had an O(mn2log n)-time algorithm for the problem on a general graph. On a tree, the time complexity of their algorithm becomes O(n2). In this paper, we improve these two bounds to O(mnlog n) and O(nlog2n), respectively.