Approximation algorithms for geometric median problems
Information Processing Letters
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Incremental clustering and dynamic information retrieval
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Cluster analysis and mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation algorithms for min-sum p-clustering
Discrete Applied Mathematics
Analysis of a local search heuristic for facility location problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Greedy strikes back: improved facility location algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for a capacitated facility location problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximating min-sum k-clustering in metric spaces
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms for clustering to minimize the sum of diameters
Nordic Journal of Computing
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Algorithms for two-box covering
Proceedings of the twenty-second annual symposium on Computational geometry
On clustering to minimize the sum of radii
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
ACM Transactions on Knowledge Discovery from Data (TKDD)
On Metric Clustering to Minimize the Sum of Radii
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
A generalized minimum cost k-clustering
ACM Transactions on Algorithms (TALG)
Locating facilities on a network to minimize their average service radius
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
The structural clustering and analysis of metric based on granular space
Pattern Recognition
Online clustering with variable sized clusters
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Multi cover of a polygon minimizing the sum of areas
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Connecting a set of circles with minimum sum of radii
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Partitioning the nodes of a graph to minimize the sum of subgraph radii
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Computer Science Review
On Clustering to Minimize the Sum of Radii
SIAM Journal on Computing
On minimum sum of radii and diameters clustering
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
A constant-factor approximation for multi-covering with disks
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We study the problem of clustering points in a metric space so as to minimize the sum of cluster diameters or the sum of cluster radii. Significantly improving on previous results, we present a primal-dual based constant factor approximation algorithm for this problem. We present a simple greedy algorithm that achieves a logarithmic approximation. This also applies when the distance function is asymmetric and the objective is to minimize the sum of cluster radii. The previous best-known result obtained a logarithmic approximation with a constant factor blowup in the number of clusters. We also obtain an incremental clustering algorithm that maintains a solution whose cost is at most a constant factor times that of optimal with a constant factor blowup in the number of clusters.