## Exact and Approximation Algortihms for Clustering (Extended Abstract) (1998)

### BibTeX

@MISC{Agarwal98exactand,

author = {Pankaj K. Agarwal and Cecilia M. Procopiuc},

title = {Exact and Approximation Algortihms for Clustering (Extended Abstract)},

year = {1998}

}

### OpenURL

### Abstract

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.