## Abstract

The min-sum k-clustering problem in a metric space is to find a partition of the space into k clusters as to minimize the total sum of distances between pairs of points assigned to the same cluster. We give the first polynomial time non-trivial approximation algorithm for this problem. The algorithm provides an O(1/ε log^{1+ε} n) approximation to the min-sum k-clustering problem in general metric spaces, with running time n^{o(1/ε)}. The result is based on embedding of metric spaces into hierarchically separated trees. We also provide a bicriteria approximation result that provides a constant approximation factor solution with only a constant factor increase in the number of clusters. This result is obtained by modifying and drawing ideas from recently developed primal dual approximation algorithms for facility location.

Original language | American English |
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Pages (from-to) | 11-20 |

Number of pages | 10 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - 2001 |

Event | 33rd Annual ACM Symposium on Theory of Computing - Creta, Greece Duration: 6 Jul 2001 → 8 Jul 2001 |