@inproceedings{c87d4a5e84d445c7a9727a4bd034ba95,
title = "On weak ϵ-nets and the radon number",
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{\textquoteright}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 an amplification result for weak -nets.",
keywords = "Abstract convexity, Haussler packing lemma, Kneser graphs, Radon number, VC dimension, Weak epsilon nets",
author = "Shay Moran and Amir Yehudayoff",
note = "Publisher Copyright: {\textcopyright} Shay Moran and Amir Yehudayoff.; 35th International Symposium on Computational Geometry, SoCG 2019 ; Conference date: 18-06-2019 Through 21-06-2019",
year = "2019",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2019.51",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
pages = "1--14",
editor = "Gill Barequet and Yusu Wang",
booktitle = "35th International Symposium on Computational Geometry, SoCG 2019",
}