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(mn 2log n)-time algorithm for the problem on a general graph. On a tree, the time complexity of their algorithm becomes O(n 2). In this paper, we improve these two bounds to O(mnlog n) and O(nlog2 n), respectively.
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Lin, TC., Yu, HI., Wang, BF. (2006). Improved Algorithms for the Minmax-Regret 1-Center Problem. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_54
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DOI: https://doi.org/10.1007/11940128_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49694-6
Online ISBN: 978-3-540-49696-0
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