Exact and Approximation Algorithms for Clustering (Extended Abstract).
Pankaj Agarwal, Cecilia M. Procopiuc · 1998
In this paper we present an n O(k 1\\Gamma1=d ) time algorithm for solving the k-center problem in R d , under L1 and L2 metrics. The algorithm extends to other metrics, and to the discrete k-center problem. We also describe a simple (1+ ffl)- approximation algorithm for the k-center problem, with running time O(n log k) + (k=ffl) O(k 1\\Gamma1=d ) . Finally, we present a n O(k 1\\Gamma1=d ) time algorithm for solving the L-capacitated k- center problem, provided that L = \\Omega\\Gamma n=k 1\\Gamma1=d ) or L = O(1). We conclude with a simple approximation algorithm for the L-capacitated k-center problem.