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(mn 2log n)-time algorithm for the problem on a general graph, and had an O(nlog2 n)-time algorithm on a tree. In this paper, we improve these two bounds to O(mn 2 + n 3log n) and O(nlog n), respectively.
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Yu, HI., Lin, TC., Wang, BF. (2006). Improved Algorithms for the Minmax Regret 1-Median Problem. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_8
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DOI: https://doi.org/10.1007/11809678_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36925-7
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