The minimal k-dispersion of point sets in high dimensions

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F19%3A00327961" target="_blank" >RIV/68407700:21340/19:00327961 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1016/j.jco.2018.10.001" target="_blank" >https://doi.org/10.1016/j.jco.2018.10.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jco.2018.10.001" target="_blank" >10.1016/j.jco.2018.10.001</a>

Jazyk výsledku
angličtina
Název v původním jazyce
The minimal k-dispersion of point sets in high dimensions
Popis výsledku v původním jazyce
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 P_n={x_1,...,x_n}subset [0,1]^d and kin{0,...,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.
Název v anglickém jazyce
The minimal k-dispersion of point sets in high dimensions
Popis výsledku anglicky
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 P_n={x_1,...,x_n}subset [0,1]^d and kin{0,...,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.

Projekt
<a href="/cs/project/GA18-00580S" target="_blank" >GA18-00580S: Prostory funkcí a aproximace</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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