---
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@
...