Small weak epsilon-nets

Boris Aronov, Franz Aurenhammer, Ferran Hurtado, Stefan Langerman, David Rappaport, Carlos Seara, Shakhar Smorodinsky

    Research output: Contribution to journalArticle

    Abstract

    Given a set P of points in the plane, a set of points Q is a weak -net with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing |P| points contains a point of Q. In this paper, we determine bounds on iS, the smallest epsilon that can be guaranteed for any P when |Q|=i, for small values of i.

    Original languageEnglish (US)
    Pages (from-to)455-462
    Number of pages8
    JournalComputational Geometry: Theory and Applications
    Volume42
    Issue number5
    DOIs
    StatePublished - Jul 2009

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    P-point
    Rectangle
    Convex Sets
    Set of points
    Family

    Keywords

    • Convex sets
    • Rectangles
    • Set systems
    • Weak epsilon-nets

    ASJC Scopus subject areas

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

    Cite this

    Aronov, B., Aurenhammer, F., Hurtado, F., Langerman, S., Rappaport, D., Seara, C., & Smorodinsky, S. (2009). Small weak epsilon-nets. Computational Geometry: Theory and Applications, 42(5), 455-462. https://doi.org/10.1016/j.comgeo.2008.02.005

    Small weak epsilon-nets. / Aronov, Boris; Aurenhammer, Franz; Hurtado, Ferran; Langerman, Stefan; Rappaport, David; Seara, Carlos; Smorodinsky, Shakhar.

    In: Computational Geometry: Theory and Applications, Vol. 42, No. 5, 07.2009, p. 455-462.

    Research output: Contribution to journalArticle

    Aronov, B, Aurenhammer, F, Hurtado, F, Langerman, S, Rappaport, D, Seara, C & Smorodinsky, S 2009, 'Small weak epsilon-nets', Computational Geometry: Theory and Applications, vol. 42, no. 5, pp. 455-462. https://doi.org/10.1016/j.comgeo.2008.02.005
    Aronov B, Aurenhammer F, Hurtado F, Langerman S, Rappaport D, Seara C et al. Small weak epsilon-nets. Computational Geometry: Theory and Applications. 2009 Jul;42(5):455-462. https://doi.org/10.1016/j.comgeo.2008.02.005
    Aronov, Boris ; Aurenhammer, Franz ; Hurtado, Ferran ; Langerman, Stefan ; Rappaport, David ; Seara, Carlos ; Smorodinsky, Shakhar. / Small weak epsilon-nets. In: Computational Geometry: Theory and Applications. 2009 ; Vol. 42, No. 5. pp. 455-462.
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