Article

Approximating min-sum k-clustering in metric spaces

Authors:

Yair Bartal,

Moses Charikar,

Danny RazAuthors Info & Claims

STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

Pages 11 - 20

https://doi.org/10.1145/380752.380754

Published: 06 July 2001 Publication History

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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 $\ratio$ approximation to the min-sum k-clustering problem in general metric spaces, with running time $\runtime$. 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.

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Approximating min-sum k-clustering in metric spaces

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STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

July 2001

755 pages

ISBN:1581133499

DOI:10.1145/380752

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Published: 06 July 2001

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On Zero-Sum Optimal Stopping Games

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