New bounds on the minimal dispersion

We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in [0,1]d. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings in certain regimes. In the case of random...

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Bibliographic Details
Published in:	Journal of Complexity Vol. 72; p. 101648
Main Authors:	Litvak, A.E., Livshyts, G.V.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-10-2022
Subjects:	Complexity Dispersion Largest empty box Torus secondary Largest empty box Torus Dispersion primary Complexity
Online Access:	Get full text
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Summary:	We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in [0,1]d. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings in certain regimes. In the case of random choice of points our bounds are sharp up to double logarithmic factor. We also apply our construction to k-dispersion.
ISSN:	0885-064X 1090-2708
DOI:	10.1016/j.jco.2022.101648