Finding Points in Convex Position in Density-Restricted Sets
A Dumitrescu, CD Tóth - arXiv preprint arXiv:2205.03437, 2022 - arxiv.org
For a finite set $ A\subset\mathbb {R}^ d $, let $\Delta (A) $ denote the spread of $ A $, which
is the ratio of the maximum pairwise distance to the minimum pairwise distance. For a
positive integer $ n $, let $\gamma_d (n) $ denote the largest integer such that any set $ A $
of $ n $ points in general position in $\mathbb {R}^ d $, satisfying $\Delta (A)\leq\alpha
n^{1/d} $ for a fixed $\alpha> 0$, contains at least $\gamma_d (n) $ points in convex
position. About $30 $ years ago, Valtr proved that $\gamma_2 (n)=\Theta (n^{1/3}) $. Since …
is the ratio of the maximum pairwise distance to the minimum pairwise distance. For a
positive integer $ n $, let $\gamma_d (n) $ denote the largest integer such that any set $ A $
of $ n $ points in general position in $\mathbb {R}^ d $, satisfying $\Delta (A)\leq\alpha
n^{1/d} $ for a fixed $\alpha> 0$, contains at least $\gamma_d (n) $ points in convex
position. About $30 $ years ago, Valtr proved that $\gamma_2 (n)=\Theta (n^{1/3}) $. Since …
[CITATION][C] Finding points in convex position in density-restricted sets. May 2022
A Dumitrescu, CD Tóth - arXiv preprint arXiv:2205.03437
Showing the best results for this search. See all results
