Exact and approximation algorithms for clustering
In this paper we present an nO(k1-1/d)-time algorithm for solving the k-center problem in ℝd, under L∞- and L2-metrics. The algorithm extends to other metrics, and to the discrete k-center problem. We also describe a simple (1 + ε)-approximation algorithm for the k-center problem, with running time O(n log k) + (k/ε)O(k1-1/d). Finally, we present an nO(k1-1/d)-time algorithm for solving the L-capacitated k-center problem, provided that L = Ω(n/k1-1/d) or L = O(1).
Agarwal, PK; Procopiuc, CM
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