### Abstract

One of our results: let X be a finite set on the plane, 0 <ε <1, then there exists a set F (a weak ε-net) of size at most 7/ε^{2} such that every convex set containing at least ε|X| elements of X intersects F. Note that the size of F is independent of the size of X.

Original language | English |
---|---|

Pages (from-to) | 189-200 |

Number of pages | 12 |

Journal | Combinatorics Probability and Computing |

Volume | 1 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1992 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics

### Cite this

*Combinatorics Probability and Computing*,

*1*(3), 189-200. https://doi.org/10.1017/S0963548300000225

**Point Selections and Weak ε-Nets for Convex Hulls.** / Alon, Noga; Bárány, Imre; Füredi, Z.; Kleitman, Daniel J.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 1, no. 3, pp. 189-200. https://doi.org/10.1017/S0963548300000225

}

TY - JOUR

T1 - Point Selections and Weak ε-Nets for Convex Hulls

AU - Alon, Noga

AU - Bárány, Imre

AU - Füredi, Z.

AU - Kleitman, Daniel J.

PY - 1992

Y1 - 1992

N2 - One of our results: let X be a finite set on the plane, 0 <ε <1, then there exists a set F (a weak ε-net) of size at most 7/ε2 such that every convex set containing at least ε|X| elements of X intersects F. Note that the size of F is independent of the size of X.

AB - One of our results: let X be a finite set on the plane, 0 <ε <1, then there exists a set F (a weak ε-net) of size at most 7/ε2 such that every convex set containing at least ε|X| elements of X intersects F. Note that the size of F is independent of the size of X.

UR - http://www.scopus.com/inward/record.url?scp=84971766257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84971766257&partnerID=8YFLogxK

U2 - 10.1017/S0963548300000225

DO - 10.1017/S0963548300000225

M3 - Article

VL - 1

SP - 189

EP - 200

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 3

ER -