Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Information retrieval: data structures and algorithms
Information retrieval: data structures and algorithms
Randomized algorithms
Dynamic and static algorithms for optimal placement of resources in a tree
Theoretical Computer Science
Sublinear time algorithms for metric space problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Subquadratic approximation algorithms for clustering problems in high dimensional spaces
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Indexing large metric spaces for similarity search queries
ACM Transactions on Database Systems (TODS)
Dimensionality reduction techniques for proximity problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Searching Multimedia Databases by Content
Searching Multimedia Databases by Content
Clustering Large Datasets in Arbitrary Metric Spaces
ICDE '99 Proceedings of the 15th International Conference on Data Engineering
Antipole Tree Indexing to Support Range Search and K-Nearest Neighbor Search in Metric Spaces
IEEE Transactions on Knowledge and Data Engineering
An Efficient Approximate Algorithm for the 1-Median Problem in Metric Spaces
SIAM Journal on Optimization
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
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Extensions of the randomized tournaments techniques introduced in [6,7] to approximate solutions of 1-median and diameter computation of finite subsets of general metric spaces are proposed. In the linear algorithms proposed in [6] (resp.[7]) randomized tournaments are played among the elements of an input subset S of a metric space. At each turn the residual set of winners is randomly partitioned in nonempty disjoint subsets of fixed size. The 1-median (resp. diameter) of each subset goes to the next turn whereas the residual elements are discarded. The algorithm proceeds recursively until a residual set of cardinality less than a given threshold is generated. The 1-median (resp. diameter) of such residual set is the approximate 1-median (resp. diameter) of the input set S. The ${\mathcal O}$(n log n) extensions proposed in this paper replace local single-winner tournaments by multiple-winners ones. Moreover consensus is introduced as multiple runs of the same tournament. Experiments on both synthetic and real data show that these new proposed versions give significantly better approximations of the exact solutions of the corresponding optimization problems.