TY - JOUR

T1 - Approximating min-sum k-clustering in metric spaces

AU - Bartal, Y.

AU - Charikar, M.

AU - Raz, D.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034825991&partnerID=8YFLogxK

U2 - 10.1145/380752.380754

DO - 10.1145/380752.380754

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AN - SCOPUS:0034825991

SN - 0734-9025

SP - 11

EP - 20

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

T2 - 33rd Annual ACM Symposium on Theory of Computing

Y2 - 6 July 2001 through 8 July 2001

ER -