A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
Algorithms for clustering data
Algorithms for clustering data
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Journal of Algorithms
BIRCH: an efficient data clustering method for very large databases
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
An approximation algorithm for clustering graphs with dominating diametral path
Information Processing Letters
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
Bicriteria network design problems
Journal of Algorithms
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
Approximation algorithms for min-sum p-clustering
Discrete Applied Mathematics
Information retrieval algorithms: a survey
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Exact and approximation algorithms for clustering
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
The budgeted maximum coverage problem
Information Processing Letters
Approximation algorithms for projective clustering
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Some geometric clustering problems
Nordic Journal of Computing
Efficient Parallel Algorithms for Geometric k-Clustering Problems
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Subspace Discovery for Promotion: A Cell Clustering Approach
DS '09 Proceedings of the 12th International Conference on Discovery Science
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We consider the problem of partitioning the nodes of a complete edge weighted graph into k clusters so as to minimize the sum of the diameters of the clusters. Since the problem is NP-complete, our focus is on the development of good approximation algorithms. When edge weights satisfy the triangle inequality, we present the first approximation algorithm for the problem. The approximation algorithm yields a solution that has no more than 10 k clusters such that the total diameter of these clusters is within a factor O (log (n/k)) of the optimal value for k clusters, where n is the number of nodes in the complete graph. For any fixed k, we present an approximation algorithm that produces k clusters whose total diameter is at most twice the optimal value. When the distances are not required to satisfy the triangle inequality, we show that, unless P = NP, for any ρ ≥ 1, there is no polynomial time approximation algorithm that can provide a performance guarantee of ρ even when the number of clusters is fixed at 3. Other results obtained include a polynomial time algorithm for the problem when the underlying graph is a tree with edge weights.