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

P. K. Agarwal, B. 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
    DOIs
    StatePublished - Apr 1998

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    ASJC Scopus subject areas

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

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