---
res:
  bibo_abstract:
  - 'Let S be a set of n points in ℝd . A set W is a weak ε-net for (convex ranges
    of)S if, for any T⊆S containing εn points, the convex hull of T intersects W.
    We show the existence of weak ε-nets of size {Mathematical expression}, where
    β2=0, β3=1, and βd ≈0.149·2d-1(d-1)!, improving a previous bound of Alon et al.
    Such a net can be computed effectively. We also consider two special cases: when
    S is a planar point set in convex position, we prove the existence of a net of
    size O((1/ε) log1.6(1/ε)). In the case where S consists of the vertices of a regular
    polygon, we use an argument from hyperbolic geometry to exhibit an optimal net
    of size O(1/ε), which improves a previous bound of Capoyleas.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Bernard
      foaf_name: Chazelle, Bernard
      foaf_surname: Chazelle
  - foaf_Person:
      foaf_givenName: Herbert
      foaf_name: Edelsbrunner, Herbert
      foaf_surname: Edelsbrunner
      foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-9823-6833
  - foaf_Person:
      foaf_givenName: Michelangelo
      foaf_name: Grigni, Michelangelo
      foaf_surname: Grigni
  - foaf_Person:
      foaf_givenName: Leonidas
      foaf_name: Guibas, Leonidas
      foaf_surname: Guibas
  - foaf_Person:
      foaf_givenName: Micha
      foaf_name: Sharir, Micha
      foaf_surname: Sharir
  - foaf_Person:
      foaf_givenName: Emo
      foaf_name: Welzl, Emo
      foaf_surname: Welzl
  bibo_doi: 10.1007/BF02574025
  bibo_issue: '1'
  bibo_volume: 13
  dct_date: 1995^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0179-5376
  dct_language: eng
  dct_publisher: Springer@
  dct_title: Improved bounds on weak ε-nets for convex sets@
...