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 language||American English|
|Number of pages||10|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|State||Published - 2001|
|Event||33rd Annual ACM Symposium on Theory of Computing - Creta, Greece|
Duration: 6 Jul 2001 → 8 Jul 2001