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- W2809782772 abstract "In this manuscript we introduce and study an extended version of the minimal dispersion of point sets, which has recently attracted considerable attention. Given a set $mathscr P_n={x_1,dots,x_n}subset [0,1]^d$ and $kin{0,1,dots,n}$, we define the $k$-dispersion to be the volume of the largest box amidst a point set containing at most $k$ points. The minimal $k$-dispersion is then given by the infimum over all possible point sets of cardinality $n$. We provide both upper and lower bounds for the minimal $k$-dispersion that coincide with the known bounds for the classical minimal dispersion for a surprisingly large range of $k$'s." @default.
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- W2809782772 date "2019-04-01" @default.
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- W2809782772 title "The minimal <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=mml1 display=inline overflow=scroll altimg=si1.gif><mml:mi>k</mml:mi></mml:math>-dispersion of point sets in high dimensions" @default.
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- W2809782772 doi "https://doi.org/10.1016/j.jco.2018.10.001" @default.
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