The number of edges of many faces in a line segment arrangement

Boris Aronov, H. Edelsbrunner, L. J. Guibas, M. Sharir

    Research output: Contribution to journalArticle

    Abstract

    We show that the maximum number of edges bounding m faces in an arrangement of n line segments in the plane is O(m2/3n2/3+nα(n)+nlog m). This improves a previous upper bound of Edelsbrunner et al. [5] and almost matches the best known lower bound which is Ω(m2/3n2/3+nα(n)). In addition, we show that the number of edges bounding any m faces in an arrangement of n line segments with a total of t intersecting pairs is O(m2/3t1/3+nα(t/n)+nmin{log m,log t/n}), almost matching the lower bound of Ω(m2/3t1/3+nα(t/n)) demonstrated in this paper.

    Original languageEnglish (US)
    Pages (from-to)261-274
    Number of pages14
    JournalCombinatorica
    Volume12
    Issue number3
    DOIs
    StatePublished - Sep 1992

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    Line segment
    Arrangement
    Face
    Lower bound
    Upper bound

    Keywords

    • AMS subject classification code (1991): 52B05, 52C10, 68U05

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Mathematics(all)

    Cite this

    Aronov, B., Edelsbrunner, H., Guibas, L. J., & Sharir, M. (1992). The number of edges of many faces in a line segment arrangement. Combinatorica, 12(3), 261-274. https://doi.org/10.1007/BF01285815

    The number of edges of many faces in a line segment arrangement. / Aronov, Boris; Edelsbrunner, H.; Guibas, L. J.; Sharir, M.

    In: Combinatorica, Vol. 12, No. 3, 09.1992, p. 261-274.

    Research output: Contribution to journalArticle

    Aronov, B, Edelsbrunner, H, Guibas, LJ & Sharir, M 1992, 'The number of edges of many faces in a line segment arrangement', Combinatorica, vol. 12, no. 3, pp. 261-274. https://doi.org/10.1007/BF01285815
    Aronov B, Edelsbrunner H, Guibas LJ, Sharir M. The number of edges of many faces in a line segment arrangement. Combinatorica. 1992 Sep;12(3):261-274. https://doi.org/10.1007/BF01285815
    Aronov, Boris ; Edelsbrunner, H. ; Guibas, L. J. ; Sharir, M. / The number of edges of many faces in a line segment arrangement. In: Combinatorica. 1992 ; Vol. 12, No. 3. pp. 261-274.
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