On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Bicriteria network design problems
Journal of Algorithms
Approximation algorithms for min-sum p-clustering
Discrete Applied Mathematics
P-Complete Approximation Problems
Journal of the ACM (JACM)
Clustering for edge-cost minimization (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Clustering to minimize the sum of cluster diameters
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Embeddings and non-approximability of geometric problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Clustering Data Streams: Theory and Practice
IEEE Transactions on Knowledge and Data Engineering
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Randomized k-server algorithms for growth-rate bounded graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Facility location with Service Installation Costs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Clustering to minimize the sum of cluster diameters
Journal of Computer and System Sciences - STOC 2001
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Approximating k-median with non-uniform capacities
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Randomized k-server algorithms for growth-rate bounded graphs
Journal of Algorithms
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A constant factor approximation algorithm for k-median clustering with outliers
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A combinatorial allocation mechanism with penalties for banner advertising
Proceedings of the 17th international conference on World Wide Web
ACM Transactions on Knowledge Discovery from Data (TKDD)
Approximate clustering without the approximation
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Text document clustering based on neighbors
Data & Knowledge Engineering
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Pairwise data clustering and applications
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Small space representations for metric min-sum k-clustering and their applications
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A uniqueness theorem for clustering
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Integer point sets minimizing average pairwise L1 distance: What is the optimal shape of a town?
Computational Geometry: Theory and Applications
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Min-sum clustering of protein sequences with limited distance information
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
Center-based clustering under perturbation stability
Information Processing Letters
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Communication-aware processor allocation for supercomputers
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Clustering under perturbation resilience
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Data stability in clustering: a closer look
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Clustering under approximation stability
Journal of the ACM (JACM)
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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.