--- 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@ ...