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A Linear time algorithm for computing the Voronoi diagram of a convex polygon

Authors:

A. Aggarwal,

L. Guibas,

J. Saxe, and

P. ShorAuthors Info & Claims

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

January 1987

Pages 39 - 45

https://doi.org/10.1145/28395.28400

Published: 01 January 1987 Publication History

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Abstract

We present an algorithm for computing certain kinds of three-dimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram of n points in the plane can be computed in Θ(n) time when these points form the vertices of a convex polygon in, say, counterclockwise order. This settles an outstanding open problem in computational geometry. Our techniques can also be used to obtain linear time algorithms for computing the farthest-point Voronoi diagram and the medial axis of a convex polygon and for deleting a vertex from a general planar Voronoi diagram.

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Cited By

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Habib FMegahed NBadawy NShahda M(2024) D 4 G framework: a novel Voronoi diagram classification for decoding natural geometrics to enhance the built environment Architectural Science Review10.1080/00038628.2024.2321584(1-28)Online publication date: Mar-2024
https://doi.org/10.1080/00038628.2024.2321584
Claverol Mde las Heras Parrilla AHuemer CMartínez-Moraian A(2024)The edge labeling of higher order Voronoi diagramsJournal of Global Optimization10.1007/s10898-024-01386-0Online publication date: 21-May-2024
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A Linear time algorithm for computing the Voronoi diagram of a convex polygon

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STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

January 1987

471 pages

ISBN:0897912217

DOI:10.1145/28395

Editor:
Alfred V. Aho

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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Association for Computing Machinery

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Published: 01 January 1987

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STOC87: 19th Annual ACM Conference on Theory of Computing

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STOC '87 Paper Acceptance Rate 50 of 165 submissions, 30%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

View all

Habib FMegahed NBadawy NShahda M(2024) D 4 G framework: a novel Voronoi diagram classification for decoding natural geometrics to enhance the built environment Architectural Science Review10.1080/00038628.2024.2321584(1-28)Online publication date: Mar-2024
https://doi.org/10.1080/00038628.2024.2321584
Claverol Mde las Heras Parrilla AHuemer CMartínez-Moraian A(2024)The edge labeling of higher order Voronoi diagramsJournal of Global Optimization10.1007/s10898-024-01386-0Online publication date: 21-May-2024
https://doi.org/10.1007/s10898-024-01386-0
Erler MKoch ABrosius A(2023)Determination of Largest Possible Cutter Diameter of End Mills for Arbitrarily Shaped 3-Axis Milling FeaturesProduction at the Leading Edge of Technology10.1007/978-3-031-18318-8_24(228-237)Online publication date: 2-Feb-2023
https://doi.org/10.1007/978-3-031-18318-8_24
Aloupis GBarba LCarufel JLangerman SSouvaine D(2015)Isoperimetric EnclosuresGraphs and Combinatorics10.1007/s00373-015-1553-231:2(361-392)Online publication date: 1-Mar-2015
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Bhattacharya A(2014)BibliographyFundamentals of Database Indexing and Searching10.1201/b17767-23(235-245)Online publication date: 5-Nov-2014
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Augustine JDas SMaheshwari ANandy SRoy SSarvattomananda S(2013)Localized geometric query problemsComputational Geometry: Theory and Applications10.1016/j.comgeo.2012.09.00946:3(340-357)Online publication date: 1-Apr-2013
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Fan CLuo JWang WZhu B(2012)Voronoi diagram with visual restrictionProceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management10.1007/978-3-642-29700-7_4(36-46)Online publication date: 14-May-2012
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Zhang PKarimpour MBalint DLin J(2012)Cohesive zone representation and junction partitioning for crystal plasticity analysesInternational Journal for Numerical Methods in Engineering10.1002/nme.435692:8(715-733)Online publication date: 12-Jun-2012
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Dinis JMamede M(2011)Updates on Voronoi DiagramsProceedings of the 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering10.1109/ISVD.2011.33(192-199)Online publication date: 28-Jun-2011
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