Line transversals of balls and smallest enclosing cylinders in three dimensions

Pankaj K. Agarwal, Boris Aronov, Micha Sharir

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

    Abstract

    We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
    Editors Anon
    PublisherACM
    Pages483-492
    Number of pages10
    StatePublished - 1997
    EventProceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA, USA
    Duration: Jan 5 1997Jan 7 1997

    Other

    OtherProceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms
    CityNew Orleans, LA, USA
    Period1/5/971/7/97

    Fingerprint

    Transversals
    Approximation algorithms
    Three-dimension
    Ball
    Computing
    Line
    Set of points
    Approximation Algorithms
    Upper bound

    ASJC Scopus subject areas

    • Chemical Health and Safety
    • Software
    • Safety, Risk, Reliability and Quality
    • Discrete Mathematics and Combinatorics

    Cite this

    Agarwal, P. K., Aronov, B., & Sharir, M. (1997). Line transversals of balls and smallest enclosing cylinders in three dimensions. In Anon (Ed.), Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 483-492). ACM.

    Line transversals of balls and smallest enclosing cylinders in three dimensions. / Agarwal, Pankaj K.; Aronov, Boris; Sharir, Micha.

    Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. ed. / Anon. ACM, 1997. p. 483-492.

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

    Agarwal, PK, Aronov, B & Sharir, M 1997, Line transversals of balls and smallest enclosing cylinders in three dimensions. in Anon (ed.), Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. ACM, pp. 483-492, Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, USA, 1/5/97.
    Agarwal PK, Aronov B, Sharir M. Line transversals of balls and smallest enclosing cylinders in three dimensions. In Anon, editor, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. ACM. 1997. p. 483-492
    Agarwal, Pankaj K. ; Aronov, Boris ; Sharir, Micha. / Line transversals of balls and smallest enclosing cylinders in three dimensions. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. editor / Anon. ACM, 1997. pp. 483-492
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