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Selecting distances in the plane

Authors:

Pankaj K. Agarwal,

Subhash SuriAuthors Info & Claims

SCG '90: Proceedings of the sixth annual symposium on Computational geometry

Pages 321 - 331

https://doi.org/10.1145/98524.98597

Published: 01 May 1990 Publication History

Abstract

We describe a randomized algorithm for computing the k^th 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 Ο(n^4/3 log ^8/3 n). A deterministic version of our procedure runs in time Ο(n^3/2 log^5/2 n). Both versions improve the previously best known upper bound of Ο(n^9/5 log^4/5 n) by Chazelle [Ch]. A simple Ο(n log n) time algorithm for computing an approximation of the median distance is also presented.

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Cited By

Benkoczi RBhattacharya BDas SSember J(2009)Single facility collection depots location problem in the planeComputational Geometry: Theory and Applications10.5555/1519530.151957442:5(403-418)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.5555/1519530.1519574
Goodrich M(1995)Efficient piecewise-linear function approximation using the uniform metricDiscrete & Computational Geometry10.1007/BF0257071714:4(445-462)Online publication date: 1-Dec-1995
https://dl.acm.org/doi/10.1007/BF02570717
Goodrich MMehlhorn K(1994)Efficient piecewise-linear function approximation using the uniform metricProceedings of the tenth annual symposium on Computational geometry10.1145/177424.178040(322-331)Online publication date: 10-Jun-1994
https://dl.acm.org/doi/10.1145/177424.178040
Show More Cited By

Index Terms

Selecting distances in the plane
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Trees
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SCG '90: Proceedings of the sixth annual symposium on Computational geometry

May 1990

371 pages

ISBN:0897913620

DOI:10.1145/98524

Chairman:
Raimund Seidel

Copyright © 1990 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 May 1990

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SOCG: 6th Annual Conference on Computational Geometry

June 7 - 9, 1990

California, Berkley, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Benkoczi RBhattacharya BDas SSember J(2009)Single facility collection depots location problem in the planeComputational Geometry: Theory and Applications10.5555/1519530.151957442:5(403-418)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.5555/1519530.1519574
Goodrich M(1995)Efficient piecewise-linear function approximation using the uniform metricDiscrete & Computational Geometry10.1007/BF0257071714:4(445-462)Online publication date: 1-Dec-1995
https://dl.acm.org/doi/10.1007/BF02570717
Goodrich MMehlhorn K(1994)Efficient piecewise-linear function approximation using the uniform metricProceedings of the tenth annual symposium on Computational geometry10.1145/177424.178040(322-331)Online publication date: 10-Jun-1994
https://dl.acm.org/doi/10.1145/177424.178040
Goodrich MMitchell JOrletsky MMehlhorn K(1994)Practical methods for approximate geometric pattern matching under rigid motionsProceedings of the tenth annual symposium on Computational geometry10.1145/177424.177572(103-112)Online publication date: 10-Jun-1994
https://dl.acm.org/doi/10.1145/177424.177572
Katz MSharir MYap C(1993)An expander-based approach to geometric optimizationProceedings of the ninth annual symposium on Computational geometry10.1145/160985.161137(198-207)Online publication date: 1-Jul-1993
https://dl.acm.org/doi/10.1145/160985.161137
Goodrich MYap C(1993)Geometric partitioning made easier, even in parallelProceedings of the ninth annual symposium on Computational geometry10.1145/160985.161002(73-82)Online publication date: 1-Jul-1993
https://dl.acm.org/doi/10.1145/160985.161002
Dickerson MShugart J(1993)A simple algorithm for enumerating longest distances in the planeInformation Processing Letters10.1016/0020-0190(93)90215-U45:5(269-274)Online publication date: 2-Apr-1993
https://dl.acm.org/doi/10.1016/0020-0190%2893%2990215-U
Agarwal PSharir MToledo SFrederickson G(1992)Applications of parametric searching in geometric optimizationProceedings of the third annual ACM-SIAM symposium on Discrete algorithms10.5555/139404.139420(72-82)Online publication date: 1-Sep-1992
https://dl.acm.org/doi/10.5555/139404.139420
Katoh NIwano KAvis D(1992)Finding k farthest pairs and k closest/farthest bichromatic pairs for points in the planeProceedings of the eighth annual symposium on Computational geometry10.1145/142675.142740(320-329)Online publication date: 1-Jul-1992
https://dl.acm.org/doi/10.1145/142675.142740
Pellegrini MAvis D(1992)Incidence and nearest-neighbor problems for lines in 3-spaceProceedings of the eighth annual symposium on Computational geometry10.1145/142675.142703(130-137)Online publication date: 1-Jul-1992
https://dl.acm.org/doi/10.1145/142675.142703
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