An optimal extension of the centerpoint theorem

Nabil H. Mustafa, Saurabh Ray

    Research output: Contribution to journalArticle

    Abstract

    We prove an optimal extension of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit all convex sets containing more than 47n points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure for finding small number of points hitting convex sets over P, yielding several improvements over previous results.

    Original languageEnglish (US)
    Pages (from-to)505-510
    Number of pages6
    JournalComputational Geometry: Theory and Applications
    Volume42
    Issue number6-7
    DOIs
    StatePublished - Aug 1 2009

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    Theorem
    Convex Sets
    Hitting Set
    Hits

    Keywords

    • Centerpoint theorem
    • Combinatorial geometry
    • Discrete geometry
    • Extremal methods
    • Hitting convex sets
    • Weak -nets

    ASJC Scopus subject areas

    • Geometry and Topology
    • Computer Science Applications
    • Control and Optimization
    • Computational Theory and Mathematics
    • Computational Mathematics

    Cite this

    An optimal extension of the centerpoint theorem. / Mustafa, Nabil H.; Ray, Saurabh.

    In: Computational Geometry: Theory and Applications, Vol. 42, No. 6-7, 01.08.2009, p. 505-510.

    Research output: Contribution to journalArticle

    Mustafa, Nabil H. ; Ray, Saurabh. / An optimal extension of the centerpoint theorem. In: Computational Geometry: Theory and Applications. 2009 ; Vol. 42, No. 6-7. pp. 505-510.
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