Explicit construction of a small epsilon-net for linear threshold functions

Yuval Rabani*, Amir Shpilka

*Corresponding author for this work

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

Abstract

We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dimension n and in 1/ε . To the best of our knowledge no such constructions were previously known. Our results match, up to the exponent of the polynomial, the bounds that are achieved by probabilistic arguments. As a corollary we also construct subsets of the binary cube that have size polynomial in n and covering radius of n/2 - c√n log n, for any constant c. This improves upon the well known construction of dual BCH codes that only guarantee covering radius of n/2 - c√n.

Original languageEnglish
Title of host publicationSTOC'09 - Proceedings of the 2009 ACM International Symposium on Theory of Computing
Pages649-658
Number of pages10
DOIs
StatePublished - 2009
Externally publishedYes
Event41st Annual ACM Symposium on Theory of Computing, STOC '09 - Bethesda, MD, United States
Duration: 31 May 20092 Jun 2009

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference41st Annual ACM Symposium on Theory of Computing, STOC '09
Country/TerritoryUnited States
CityBethesda, MD
Period31/05/092/06/09

Keywords

  • Epsilon-net
  • Explicit construction
  • Linear threshold function

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