On weak ϵ-nets and the radon number

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 an amplification result for weak -nets.

Original languageEnglish
Title of host publication35th International Symposium on Computational Geometry, SoCG 2019
EditorsGill Barequet, Yusu Wang
Pages1-14
ISBN (Electronic)9783959771047
DOIs
StatePublished - 1 Jun 2019
Event35th International Symposium on Computational Geometry, SoCG 2019 - Portland, United States
Duration: 18 Jun 201921 Jun 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume129

Conference

Conference35th International Symposium on Computational Geometry, SoCG 2019
Country/TerritoryUnited States
CityPortland
Period18/06/1921/06/19

Keywords

  • Abstract convexity
  • Haussler packing lemma
  • Kneser graphs
  • Radon number
  • VC dimension
  • Weak epsilon nets

All Science Journal Classification (ASJC) codes

  • Software

Fingerprint

Dive into the research topics of 'On weak ϵ-nets and the radon number'. Together they form a unique fingerprint.

Cite this