Abstract
Given a set V of n points andthe distances between each pair, the k-center problem asks us to choose a subset C ⊆ V of size k that minimizes the maximum over all points of the distance from C to the point. This problem is NP-hardev en when the distances are symmetric andsatisfy the triangle inequality, andHo chbaum andShmo ys gave a best-possible 2-approximation for this case.
We consider the version where the distances are asymmetric. Panigrahy andVish wanathan gave an O(log* n)-approximation for this case, leading many to believe that a constant approximation factor shouldb e possible. Their approach is purely combinatorial. We show how to use a natural linear programming relaxation to define a promising new measure of progress, anduse it to obtain two different O(log* k)-approximation algorithms. There is hope of obtaining further improvement from this LP, since we do not know of an instance where it has an integrality gap worse than 3.
Supported by the Fannie and John Hertz Foundation and ONR grant AASERT N0014-97-10681.
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Archer, A. (2001). Two O(log* k)-Approximation Algorithms for the Asymmetric k-Center Problem. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_1
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DOI: https://doi.org/10.1007/3-540-45535-3_1
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