## Exact and Approximation Algorithms for Clustering (1997)

Citations: | 57 - 5 self |

### BibTeX

@MISC{Agarwal97exactand,

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

title = {Exact and Approximation Algorithms for Clustering},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we present a n O(k 1\Gamma1=d ) time algorithm for solving the k-center problem in R d , under L1 and L 2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete k-center problem, as well. 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.