Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications

Micha Sharir

doi:10.1007/3-540-60220-8_55

Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications

Micha Sharir

School of Computer Science and AI

New York University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to motion planning, Voronoi diagrams, visibility, and geometric optimization.

Original language	English
Title of host publication	Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings
Editors	Selim G. Akl, Frank Dehne, Jörg-Rüdiger Sack, Nicola Santoro
Publisher	Springer Verlag
Pages	109-121
Number of pages	13
ISBN (Print)	3540602208, 9783540602200
DOIs	https://doi.org/10.1007/3-540-60220-8_55
State	Published - 1995
Event	4th Workshop on Algorithms and Data Structures, WADS 1995 - Kingston, Canada Duration: 16 Aug 1995 → 18 Aug 1995

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	955
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th Workshop on Algorithms and Data Structures, WADS 1995
Country/Territory	Canada
City	Kingston
Period	16/08/95 → 18/08/95

Funding

Funders	Funder number
National Science Foundation	CCR-93-11127, CCR-91-22103

Access to Document

10.1007/3-540-60220-8_55

Cite this

Sharir, M. (1995). Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications. In S. G. Akl, F. Dehne, J.-R. Sack, & N. Santoro (Eds.), Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings (pp. 109-121). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955). Springer Verlag. https://doi.org/10.1007/3-540-60220-8_55

Sharir, Micha. / Arrangements in higher dimensions : Voronoi diagrams, motion planning, and other applications. Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. editor / Selim G. Akl ; Frank Dehne ; Jörg-Rüdiger Sack ; Nicola Santoro. Springer Verlag, 1995. pp. 109-121 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to motion planning, Voronoi diagrams, visibility, and geometric optimization.",

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Sharir, M 1995, Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications. in SG Akl, F Dehne, J-R Sack & N Santoro (eds), Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 955, Springer Verlag, pp. 109-121, 4th Workshop on Algorithms and Data Structures, WADS 1995, Kingston, Canada, 16/08/95. https://doi.org/10.1007/3-540-60220-8_55

Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications. / Sharir, Micha.
Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. ed. / Selim G. Akl; Frank Dehne; Jörg-Rüdiger Sack; Nicola Santoro. Springer Verlag, 1995. p. 109-121 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to motion planning, Voronoi diagrams, visibility, and geometric optimization.

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Sharir M. Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications. In Akl SG, Dehne F, Sack JR, Santoro N, editors, Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. Springer Verlag. 1995. p. 109-121. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-60220-8_55

Arrangements in higher dimensions: Voronoi diagrams, motion planning, and other applications

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