Computational geometry: an introduction
Computational geometry: an introduction
Edge-skeletons in arrangements with applications
Algorithmica
Planning, geometry, and complexity of robot motion
Planning, geometry, and complexity of robot motion
An improved algorithm for constructing kth-order voronoi diagrams
IEEE Transactions on Computers
L-infinity interdistance selection by parametric search
Information Processing Letters
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Selecting distances in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Finding k points with minimum diameter and related problems
Journal of Algorithms
Enumerating k distances for n points in the plane
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
New techniques for computing order statistics in Euclidean space (extended abstract)
SCG '85 Proceedings of the first annual symposium on Computational geometry
Approximate k -Closest-Pairs with Space Filling Curves
DaWaK 2000 Proceedings of the 4th International Conference on Data Warehousing and Knowledge Discovery
An approximate algorithm for top-k closest pairs join query in large high dimensional data
Data & Knowledge Engineering
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We study the problem of enumerating k farthest pairs for n points in the plane and the problems of enumerating k closest/farthest bichromatic pairs of n red and n blue points in the plane. We propose a new technique for geometric enumeration problems which iteratively reduces the search space by a half and provides efficient algorithms. As applications of this technique, we develop algorithms, using higher order Voronoi diagrams, for the above problems, which run in O(min{n2, n log n + k4/3 log n/log1/3 k}) time and O(n+k4/3/(log k)1/3+k log n) space. Since, to the authors' knowledge, no nontrivial algorithms have been known for these problems, our algorithms are currently fastest when k=o(n3/2).