On weak $\epsilon$-nets and the Radon number
Combinatorics
2019-03-01 v3 Computational Geometry
Discrete Mathematics
Abstract
We show that the Radon number characterizes the existence of weak nets in separable convexity spaces (an abstraction of the euclidean notion of convexity). The construction of weak nets when the Radon number is finite is based on Helly's property and on metric properties of VC classes. The lower bound on the size of weak nets when the Radon number is large relies on the chromatic number of the Kneser graph. As an application, we prove a boosting-type result for weak -nets.
Keywords
Cite
@article{arxiv.1707.05381,
title = {On weak $\epsilon$-nets and the Radon number},
author = {Shay Moran and Amir Yehudayoff},
journal= {arXiv preprint arXiv:1707.05381},
year = {2019}
}
Comments
Accepted to SoCG '19, modified according to comments by reviewers