New existence proofs for ε-nets

Evangelia Pyrga, Saurabh Ray

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We describe a new technique for proving the existence of small e-nets for hypergraphs satisfying certain simple conditions. The technique is particularly useful for proving O(1/ε log 1/ε) upper bounds which is not possible using the standard VC dimension theory. We apply the technique to several geometric hypergraphs and obtain simple proofs for the existence of ( ε1) size ε-nets for them. This includes the geometric hypergraph in wdiich the vertex set is a set of points in the plane and the hyperedges are defined by a set of pseudo-disks. This result was not known previously. We also get a very short proof for the existence of O( ε1/ε) size ε-nets for halfspaces in Double strok R sign.

Original languageEnglish (US)
Title of host publicationProceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08
Pages199-207
Number of pages9
DOIs
StatePublished - Dec 12 2008
Event24th Annual Symposium on Computational Geometry, SCG'08 - College Park, MD, United States
Duration: Jun 9 2008Jun 11 2008

Other

Other24th Annual Symposium on Computational Geometry, SCG'08
CountryUnited States
CityCollege Park, MD
Period6/9/086/11/08

Fingerprint

Hypergraph
VC Dimension
Dimension Theory
Half-space
Set of points
Upper bound
Vertex of a graph

Keywords

  • Discrete geometry
  • Hitting sets
  • Hypergraph transversals
  • Strong ε-nets

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Pyrga, E., & Ray, S. (2008). New existence proofs for ε-nets. In Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08 (pp. 199-207) https://doi.org/10.1145/1377676.1377708

New existence proofs for ε-nets. / Pyrga, Evangelia; Ray, Saurabh.

Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08. 2008. p. 199-207.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pyrga, E & Ray, S 2008, New existence proofs for ε-nets. in Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08. pp. 199-207, 24th Annual Symposium on Computational Geometry, SCG'08, College Park, MD, United States, 6/9/08. https://doi.org/10.1145/1377676.1377708
Pyrga E, Ray S. New existence proofs for ε-nets. In Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08. 2008. p. 199-207 https://doi.org/10.1145/1377676.1377708
Pyrga, Evangelia ; Ray, Saurabh. / New existence proofs for ε-nets. Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08. 2008. pp. 199-207
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