Speaker
Mr
Matěj Trödler
Description
This research delves into the dispersion of point sets within a unit cube
$[0,1]^𝑑$, a measure of how well-distributed points are in a space. Building on the work of Hlawka and Niederreiter, we present improved lower bounds for minimal dispersion by constructing specific sets called restriction sets. Our approach involves analyzing test boxes, uncoverable sets, and cover-free families, leading to new bounds and insights into point distribution. Additionally, we introduce a generalized framework for restriction sets and uncoverable intersections, enhancing the understanding of high-dimensional integration. This research also has practical applications in data mining, particularly in exploring empty regions within datasets.
Author
Mr
Matěj Trödler
Co-author
Jan Vybíral