article

Diameter, width, closest line pair, and parametric searching

Authors:

Bernard Chazelle,

Herbert Edelsbrunner,

Leonidas Guibas,

Micha SharirAuthors Info & Claims

Discrete & Computational Geometry, Volume 10, Issue 2

Pages 183 - 196

https://doi.org/10.1007/BF02573973

Published: 01 December 1993 Publication History

Abstract

We apply Megiddo's parametric searching technique to several geometric optimization problems and derive significantly improved solutions for them. We obtain, for any fixed >0, anO(n1+ ) algorithm for computing the diameter of a point set in 3-space, anO(8/5+ ) algorithm for computing the width of such a set, and onO(n8/5+ ) algorithm for computing the closest pair in a set ofn lines in space. All these algorithms are deterministic.

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Ahn TChung CAhn HBae SCheong OYoon S(2024)Minimum-Width Double-Slabs and Widest Empty Slabs in High DimensionsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_20(303-317)Online publication date: 18-Mar-2024
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Published In

cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 10, Issue 2

August 1993

118 pages

ISSN:0179-5376

Issue’s Table of Contents

Copyright © Copyright © 1993 Springer-Verlag New York Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1993

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Cited By

Ahn TChung CAhn HBae SCheong OYoon S(2024)Minimum-Width Double-Slabs and Widest Empty Slabs in High DimensionsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_20(303-317)Online publication date: 18-Mar-2024
https://dl.acm.org/doi/10.1007/978-3-031-55598-5_20
Lee D(2010)Computational geometry IIAlgorithms and theory of computation handbook10.5555/1882723.1882725(2-2)Online publication date: 1-Jan-2010
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Koltun V(2004)Almost tight upper bounds for vertical decompositions in four dimensionsJournal of the ACM10.1145/1017460.101746151:5(699-730)Online publication date: 1-Sep-2004
https://dl.acm.org/doi/10.1145/1017460.1017461
Finocchiaro DPellegrini M(2002)On computing the diameter of a point set in high dimensional Euclidean spaceTheoretical Computer Science10.1016/S0304-3975(01)00258-4287:2(501-514)Online publication date: 28-Sep-2002
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Ramos E(2001)An Optimal Deterministic Algorithm for Computing the Diameter of a Three-Dimensional Point SetDiscrete & Computational Geometry10.1007/s00454-001-0029-826:2(233-244)Online publication date: 1-Feb-2001
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Agarwal PGuibas LHar-Peled SRabinovitch ASharir M(2000)Penetration depth of two convex polytopes in 3DNordic Journal of Computing10.5555/642992.6429997:3(227-240)Online publication date: 1-Sep-2000
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Chan TCheng SCheong OAgarwal PFortune S(2000)Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulusProceedings of the sixteenth annual symposium on Computational geometry10.1145/336154.336216(300-309)Online publication date: 1-May-2000
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Ramos ECheng SCheong OAgarwal PFortune S(2000)Deterministic algorithms for 3-D diameter and some 2-D lower envelopesProceedings of the sixteenth annual symposium on Computational geometry10.1145/336154.336215(290-299)Online publication date: 1-May-2000
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Eppstein D(2000)Incremental and Decremental Maintenance of Planar WidthJournal of Algorithms10.1006/jagm.2000.110737:2(570-577)Online publication date: 1-Nov-2000
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Finocchiaro DPellegrini M(1999)On Computing the Diameter of a Point Set in High Dimensional Euclidean SpaceProceedings of the 7th Annual European Symposium on Algorithms10.5555/647909.740154(365-377)Online publication date: 16-Jul-1999
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