Approximating min-sum k-clustering in metric spaces

Y. Bartal*, M. Charikar, D. Raz

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

74 Scopus citations

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 log1+ε n) approximation to the min-sum k-clustering problem in general metric spaces, with running time no(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 languageAmerican English
Pages (from-to)11-20
Number of pages10
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs
StatePublished - 2001
Event33rd Annual ACM Symposium on Theory of Computing - Creta, Greece
Duration: 6 Jul 20018 Jul 2001

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