Computational geometry: an introduction
Computational geometry: an introduction
Computing
Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Deterministic coin tossing with applications to optimal parallel list ranking
Information and Control
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Selection problems in computational geometry
Selection problems in computational geometry
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
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
Cutting hyperplane arrangements
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Journal of the ACM (JACM)
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
New techniques for computing order statistics in Euclidean space (extended abstract)
SCG '85 Proceedings of the first annual symposium on Computational geometry
Arrangements of Curves in the Plane - Topology, Combinatorics, and Algorithms
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Optimal Parallel Algorithms for Transitive Closure and Point Location in Planar Structures
Optimal Parallel Algorithms for Transitive Closure and Point Location in Planar Structures
Counting circular arc intersections
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Enumerating k distances for n points in the plane
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Planar geometric location problems and maintaining the width of a planar set
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Diameter, width, closest line pair, and parametric searching
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Incidence and nearest-neighbor problems for lines in 3-space
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Finding k farthest pairs and k closest/farthest bichromatic pairs for points in the plane
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An expander-based approach to geometric optimization
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient piecewise-linear function approximation using the uniform metric: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Single facility collection depots location problem in the plane
Computational Geometry: Theory and Applications
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We describe a randomized algorithm for computing the kth smallest distance in a set of n points in the plane, based on the parametric search technique of Megiddo [Me1]. The expected running time of our algorithm is &Ogr;(n4/3 log 8/3 n). A deterministic version of our procedure runs in time &Ogr;(n3/2 log5/2 n). Both versions improve the previously best known upper bound of &Ogr;(n9/5 log4/5 n) by Chazelle [Ch]. A simple &Ogr;(n log n) time algorithm for computing an approximation of the median distance is also presented.