On the zone of a surface in a hyperplane arrangement

Boris Aronov, Micha Sharir

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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).

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings
    PublisherSpringer Verlag
    Pages13-19
    Number of pages7
    Volume519 LNCS
    ISBN (Print)9783540475668
    DOIs
    StatePublished - 1991
    Event2nd Workshop on Algorithms and Data Structures, WADS 1991 - Ottawa, Canada
    Duration: Aug 14 1991Aug 16 1991

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume519 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other2nd Workshop on Algorithms and Data Structures, WADS 1991
    CountryCanada
    CityOttawa
    Period8/14/918/16/91

    Fingerprint

    Hyperplane Arrangement
    Algebraic Surfaces
    Cell
    Convex Body
    Hyperplane
    Arrangement
    Face
    Denote

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Aronov, B., & Sharir, M. (1991). On the zone of a surface in a hyperplane arrangement. In Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings (Vol. 519 LNCS, 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

    On the zone of a surface in a hyperplane arrangement. / Aronov, Boris; Sharir, Micha.

    Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings. Vol. 519 LNCS 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 proceedingConference contribution

    Aronov, B & Sharir, M 1991, On the zone of a surface in a hyperplane arrangement. in Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings. vol. 519 LNCS, 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, 8/14/91. https://doi.org/10.1007/BFb0028245
    Aronov B, Sharir M. On the zone of a surface in a hyperplane arrangement. In Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings. Vol. 519 LNCS. Springer Verlag. 1991. p. 13-19. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). 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. Vol. 519 LNCS 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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