and Approximation Algortihms for Clustering * (Extended Abstract) Pankaj K. Agarwal t In this paper we present an n"(k'-"d) time algorithm for solving the k-center problem in Rd, under L, and Lz metrics. The algorithm extends to other metrics, and to the discrete k-center problem. We also describe a simple (1 + E)-approximation algorithm for the k-center problem, with running time O(n log k) + (k/e)"("l-l'd). Finally, we present a nO(kl-l/d) time algorithm for solving the L-capacitated kcenter problem, provided that L = R(n/k~'-"~) or L = O(1). We conclude with a simple approximation algorithm for the L-capacitated k-center problem.
For the p-center problem, Agarwal and Procopiuc REF obtain (1 + ε)-approximation in time O(n log p) + (p/ε) O(Dp 1−1/D ) .
Exact and approximation algorithms for clustering
SODA '98
Mathematics Computer Science