On levels in arrangements of lines, segments, planes, and triangles

P. K. Agarwal, Boris Aronov, T. M. Chan, M. Sharir

    Research output: Contribution to journalArticle

    Abstract

    We consider the problem of bounding the complexity of the kth level in an arrangement of n curves or surfaces, a problem dual to, and an extension of, the well-known k-set problem. Among other results, we prove a new bound, O(nk5/3), on the complexity of the kth level in an arrangement of n planes in ℝ3, or on the number of k-sets in a set of n points in three dimensions, and we show that the complexity of the kth level in an arrangement of n line segments in the plane is O(n-√kα(n/k)), and that the complexity of the kth level in an arrangement of n triangles in 3-space is O(n2k5/6α(n/k)).

    Original languageEnglish (US)
    Pages (from-to)315-331
    Number of pages17
    JournalDiscrete and Computational Geometry
    Volume19
    Issue number3
    StatePublished - 1998

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    Line segment
    Triangle
    Arrangement
    Dual Problem
    Three-dimension
    Curve

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Discrete Mathematics and Combinatorics
    • Geometry and Topology

    Cite this

    Agarwal, P. K., Aronov, B., Chan, T. M., & Sharir, M. (1998). On levels in arrangements of lines, segments, planes, and triangles. Discrete and Computational Geometry, 19(3), 315-331.

    On levels in arrangements of lines, segments, planes, and triangles. / Agarwal, P. K.; Aronov, Boris; Chan, T. M.; Sharir, M.

    In: Discrete and Computational Geometry, Vol. 19, No. 3, 1998, p. 315-331.

    Research output: Contribution to journalArticle

    Agarwal, PK, Aronov, B, Chan, TM & Sharir, M 1998, 'On levels in arrangements of lines, segments, planes, and triangles', Discrete and Computational Geometry, vol. 19, no. 3, pp. 315-331.
    Agarwal, P. K. ; Aronov, Boris ; Chan, T. M. ; Sharir, M. / On levels in arrangements of lines, segments, planes, and triangles. In: Discrete and Computational Geometry. 1998 ; Vol. 19, No. 3. pp. 315-331.
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