On the zone of a surface in a hyperplane arrangement

Boris Aronov; Micha Sharir

doi:10.1007/BFb0028245

On the zone of a surface in a hyperplane arrangement

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

Abstract

Let H be a collection of n hyperplanes in ℝd, let A denote the arrangement of H, and let σ be a (d - 1)-dimensional algebraic surface of low degree, or the boundary of a convex body in ℝ^d. The zone of σ in A is the collection of cells of A crossed by σ. We show that the total number of faces bounding the cells of the zone of σ is O(n^d−1 log n).

Original language	English
Title of host publication	Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings
Editors	Frank Dehne, Jorg-Rudiger Sack, Nicola Santoro
Publisher	Springer Verlag
Pages	13-19
Number of pages	7
ISBN (Print)	9783540475668
DOIs	https://doi.org/10.1007/BFb0028245
State	Published - 1991
Externally published	Yes
Event	2nd Workshop on Algorithms and Data Structures, WADS 1991 - Ottawa, Canada Duration: 14 Aug 1991 → 16 Aug 1991

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	519 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	2nd Workshop on Algorithms and Data Structures, WADS 1991
Country/Territory	Canada
City	Ottawa
Period	14/08/91 → 16/08/91

Access to Document

10.1007/BFb0028245

Cite this

Aronov, B., & Sharir, M. (1991). On the zone of a surface in a hyperplane arrangement. In F. Dehne, J-R. Sack, & N. Santoro (Eds.), Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings (pp. 13-19). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 519 LNCS). Springer Verlag. https://doi.org/10.1007/BFb0028245

Aronov, Boris ; Sharir, Micha. / On the zone of a surface in a hyperplane arrangement. Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings. editor / Frank Dehne ; Jorg-Rudiger Sack ; Nicola Santoro. Springer Verlag, 1991. pp. 13-19 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Let H be a collection of n hyperplanes in ℝd, let A denote the arrangement of H, and let σ be a (d - 1)-dimensional algebraic surface of low degree, or the boundary of a convex body in ℝd. The zone of σ in A is the collection of cells of A crossed by σ. We show that the total number of faces bounding the cells of the zone of σ is O(nd−1 log n).",

author = "Boris Aronov and Micha Sharir",

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year = "1991",

doi = "10.1007/BFb0028245",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Aronov, B & Sharir, M 1991, On the zone of a surface in a hyperplane arrangement. in F Dehne, J-R Sack & N Santoro (eds), Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 519 LNCS, Springer Verlag, pp. 13-19, 2nd Workshop on Algorithms and Data Structures, WADS 1991, Ottawa, Canada, 14/08/91. https://doi.org/10.1007/BFb0028245

On the zone of a surface in a hyperplane arrangement. / Aronov, Boris; Sharir, Micha.
Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings. ed. / Frank Dehne; Jorg-Rudiger Sack; Nicola Santoro. Springer Verlag, 1991. p. 13-19 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 519 LNCS).

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

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T2 - 2nd Workshop on Algorithms and Data Structures, WADS 1991

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Aronov B, Sharir M. On the zone of a surface in a hyperplane arrangement. In Dehne F, Sack J-R, Santoro N, editors, Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings. Springer Verlag. 1991. p. 13-19. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/BFb0028245

On the zone of a surface in a hyperplane arrangement

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