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License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.51
URN: urn:nbn:de:0030-drops-104551
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10455/
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Moran, Shay ; Yehudayoff, Amir

On Weak epsilon-Nets and the Radon Number

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LIPIcs-SoCG-2019-51.pdf (0.5 MB)

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 epsilon-nets.

BibTeX - Entry

@InProceedings{moran_et_al:LIPIcs:2019:10455,
  author =	{Shay Moran and Amir Yehudayoff},
  title =	{{On Weak epsilon-Nets and the Radon Number}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10455},
  URN =		{urn:nbn:de:0030-drops-104551},
  doi =		{10.4230/LIPIcs.SoCG.2019.51},
  annote =	{Keywords: abstract convexity, weak epsilon nets, Radon number, VC dimension, Haussler packing lemma, Kneser graphs}
}

Keywords: abstract convexity, weak epsilon nets, Radon number, VC dimension, Haussler packing lemma, Kneser graphs
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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