Improved bounds for the union of locally fat objects in the plane

Boris Aronov, Mark De Berg, Esther Ezrar, Micha Sharir

    Research output: Contribution to journalArticle

    Abstract

    We show that, for any γ > 0, the combinatorial complexity of the union of n locally γ-fat objects of constant complexity in the plane is nγ4 2O(log n). For the special case of γ-fat triangles,the bound improves to O(n log n + n/γ log2 1/γ ).

    Original languageEnglish (US)
    Pages (from-to)543-572
    Number of pages30
    JournalSIAM Journal on Computing
    Volume43
    Issue number2
    DOIs
    StatePublished - 2014

    Fingerprint

    Fat Objects
    Combinatorial Complexity
    Oils and fats
    Triangle
    Union

    Keywords

    • Combinatorial geometry
    • Fat objects
    • Union complexity

    ASJC Scopus subject areas

    • Mathematics(all)
    • Computer Science(all)

    Cite this

    Improved bounds for the union of locally fat objects in the plane. / Aronov, Boris; De Berg, Mark; Ezrar, Esther; Sharir, Micha.

    In: SIAM Journal on Computing, Vol. 43, No. 2, 2014, p. 543-572.

    Research output: Contribution to journalArticle

    Aronov, B, De Berg, M, Ezrar, E & Sharir, M 2014, 'Improved bounds for the union of locally fat objects in the plane', SIAM Journal on Computing, vol. 43, no. 2, pp. 543-572. https://doi.org/10.1137/120891241
    Aronov, Boris ; De Berg, Mark ; Ezrar, Esther ; Sharir, Micha. / Improved bounds for the union of locally fat objects in the plane. In: SIAM Journal on Computing. 2014 ; Vol. 43, No. 2. pp. 543-572.
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