Weak -nets have basis of size o(1/ log (1/)) in any dimension

Nabil Mustafa, Saurabh Ray

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Given a set P of n points in Rd and > 0, we consider the problemof constructing weak -nets for P.We show the following: pick a random sample Q of size O(1/ log (1/)) from P. Then, with constant probability, a weak -net of P can be constructed from only the points of Q. This shows that weak -nets in Rd can be computed from a subset of P of size O(1/ log(1/)) with only the constant of proportionality depending on the dimension, unlike all previous work where the size of the subset had the dimension in the exponent of 1/. However, our final weak -nets still have a large size (with the dimension appearing in the exponent of 1/).

    Original languageEnglish (US)
    Title of host publicationProceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07
    Pages239-244
    Number of pages6
    DOIs
    StatePublished - Oct 22 2007
    Event23rd Annual Symposium on Computational Geometry, SCG'07 - Gyeongju, Korea, Republic of
    Duration: Jun 6 2007Jun 8 2007

    Other

    Other23rd Annual Symposium on Computational Geometry, SCG'07
    CountryKorea, Republic of
    CityGyeongju
    Period6/6/076/8/07

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    Keywords

    • Combinatorial geometry
    • Discrete geometry
    • Hitting convex sets
    • Weak epsilon nets

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Computational Mathematics

    Cite this

    Mustafa, N., & Ray, S. (2007). Weak -nets have basis of size o(1/ log (1/)) in any dimension. In Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07 (pp. 239-244) https://doi.org/10.1145/1247069.1247113

    Weak -nets have basis of size o(1/ log (1/)) in any dimension. / Mustafa, Nabil; Ray, Saurabh.

    Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. 2007. p. 239-244.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Mustafa, N & Ray, S 2007, Weak -nets have basis of size o(1/ log (1/)) in any dimension. in Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. pp. 239-244, 23rd Annual Symposium on Computational Geometry, SCG'07, Gyeongju, Korea, Republic of, 6/6/07. https://doi.org/10.1145/1247069.1247113
    Mustafa N, Ray S. Weak -nets have basis of size o(1/ log (1/)) in any dimension. In Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. 2007. p. 239-244 https://doi.org/10.1145/1247069.1247113
    Mustafa, Nabil ; Ray, Saurabh. / Weak -nets have basis of size o(1/ log (1/)) in any dimension. Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. 2007. pp. 239-244
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