Randomized algorithms
Fast multiresolution image querying
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Construction of 1-d lower envelopes and applications
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Subquadratic approximation algorithms for clustering problems in high dimensional spaces
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An efficient algorithm for the three-dimensional diameter problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A Theory of Learning and Generalization: With Applications to Neural Networks and Control Systems
A Theory of Learning and Generalization: With Applications to Neural Networks and Control Systems
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Better algorithms for high-dimensional proximity problems via asymmetric embeddings
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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We consider the problem of computing the diameter of a set of n points in d-dimensional Euclidean space under Euclidean distance function. We describe an algorithm that in time O(dn log n+n2) finds with high probability an arbitrarily close approximation of the diameter. For large values of d the complexity bound of our algorithm is a substantial improvement over the complexity bounds of previously known exact algorithms. Computing and approximating the diameter are fundamental primitives in high dimensional computational geometry and find practical application, for example, in clustering operations for image databases.