Improved algorithms for the minmax regret 1-median problem

Authors:
Hung-I Yu;Tzu-Chin Lin;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:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

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Abstract

This paper studies the problem of finding the 1-median 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, and had an O(nlog2n)-time algorithm on a tree. In this paper, we improve these two bounds to O(mn2 + n3log n) and O(nlog n), respectively.