Cutting circles into pseudo-segments and improved bounds for incidences

Boris Aronov, Micha Sharir

    Research output: Contribution to journalArticle

    Abstract

    We show that n arbitrary circles in the plane can be cut into O(n3/2+ε) arcs, for any ε > 0, such that any pair of arcs intersects at most once. This improves a recent result of Tamaki and Tokuyama [20]. We use this result to obtain improved upper bounds on the number of incidences between m points and n circles. An improved incidence bound is also obtained for graphs of polynomials of any constant maximum degree.

    Original languageEnglish (US)
    Pages (from-to)475-490
    Number of pages16
    JournalDiscrete and Computational Geometry
    Volume28
    Issue number4
    DOIs
    StatePublished - 2002

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    Incidence
    Arc of a curve
    Circle
    Polynomials
    Intersect
    Maximum Degree
    Upper bound
    Polynomial
    Arbitrary
    Graph in graph theory

    ASJC Scopus subject areas

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

    Cite this

    Cutting circles into pseudo-segments and improved bounds for incidences. / Aronov, Boris; Sharir, Micha.

    In: Discrete and Computational Geometry, Vol. 28, No. 4, 2002, p. 475-490.

    Research output: Contribution to journalArticle

    Aronov, Boris ; Sharir, Micha. / Cutting circles into pseudo-segments and improved bounds for incidences. In: Discrete and Computational Geometry. 2002 ; Vol. 28, No. 4. pp. 475-490.
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