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A lower bound for the dispersion on the torus

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  • Ullrich, Mario

Abstract

We consider the volume of the largest axis-parallel box in the d-dimensional torus that contains no point of a given point set Pn with n elements. We prove that, for all natural numbers d,n and every point set Pn, this volume is bounded from below by min{1,d/n}. This implies the same lower bound for the discrepancy on the torus.

Suggested Citation

  • Ullrich, Mario, 2018. "A lower bound for the dispersion on the torus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 186-190.
    • Handle: RePEc:eee:matcom:v:143:y:2018:i:c:p:186-190
    DOI: 10.1016/j.matcom.2015.12.005
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    References listed on IDEAS

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    1. Sidney Yakowitz & Pierre L'Ecuyer & Felisa Vázquez-Abad, 2000. "Global Stochastic Optimization with Low-Dispersion Point Sets," Operations Research, INFORMS, vol. 48(6), pages 939-950, December.
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    More about this item

    Keywords

    Dispersion; Discrepancy; Torus;
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