Abstract
In this paper we present an n^ O(k 1-1/d ) -time algorithm for solving the k -center problem in \reals d , under L ∈ fty - and L 2 -metrics. The algorithm extends to other metrics, and to the discrete k -center problem. We also describe a simple (1+ɛ) -approximation algorithm for the k -center problem, with running time O(nlog k) + (k/ɛ)^ O(k 1-1/d ) . Finally, we present an n^ O(k 1-1/d ) -time algorithm for solving the L -capacitated k -center problem, provided that L=Ω(n/k 1-1/d ) or L=O(1) .
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Received July 25, 2000; revised April 6, 2001.
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Agarwal, P., Procopiuc, C. Exact and Approximation Algorithms for Clustering. Algorithmica 33, 201–226 (2002). https://doi.org/10.1007/s00453-001-0110-y
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DOI: https://doi.org/10.1007/s00453-001-0110-y