Computational geometry: an introduction
Computational geometry: an introduction
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The Johnson-Lindenstrauss Lemma and the sphericity of some graphs
Journal of Combinatorial Theory Series A
Approximating the diameter of a set of points in the Euclidean space
Information Processing Letters
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Inner and outer j-radii of convex bodies in finite-dimensional normed spaces
Discrete & Computational Geometry
A deterministic algorithm for the three-dimensional diameter problem
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces
Mathematical Programming: Series A and B
On the complexity of some basic problems in computational convexity: I.: containment problems
Discrete Mathematics - Special issue: trends in discrete mathematics
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
Syntactic clustering of the Web
Selected papers from the sixth international conference on World Wide Web
Handbook of discrete and 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
New techniques for some dynamic closest-point and farthest-point problems
SODA '90 Proceedings of the first 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
Clustering Algorithms
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Quantum speed-up for unsupervised learning
Machine Learning
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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(dnlogn + 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.