Computational geometry: an introduction
Computational geometry: an introduction
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Enumerating k distances for n points in the plane
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Maintaining the minimal distance of a point set in polylogarithmic time
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
An Onlognloglogn algorithm for the on-line closest pair problem
SODA '92 Proceedings of the third 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
Design of Dynamic Data Structures
Design of Dynamic Data Structures
Rectangular Point Location and the Dynamic Closest Pair Problem
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Divide-and-conquer in multidimensional space
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
New techniques for exact and approximate dynamic closest-point problems
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
An optimal algorithm for closest pair maintenance (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Randomized data structures for the dynamic closest-pair problem
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Fast hierarchical clustering and other applications of dynamic closest pairs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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We give an algorithm that computes the closest pair in a set of n points in k-dimensional space on-line, in O(n log n) time. The algorithm only uses algebraic functions and, therefore, is optimal. The algorithm maintains a hierarchical subdivision of k-sapce into hyper-rectangles, which is stored in a binary tree. Centroids are used to maintain a balanced decomposition of this tree.