### Abstract

Given a set P of points in the plane, a set of points Q is a weak -net with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing |P| points contains a point of Q. In this paper, we determine bounds on iS, the smallest epsilon that can be guaranteed for any P when |Q|=i, for small values of i.

Original language | English (US) |
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Pages (from-to) | 455-462 |

Number of pages | 8 |

Journal | Computational Geometry: Theory and Applications |

Volume | 42 |

Issue number | 5 |

DOIs | |

State | Published - Jul 1 2009 |

### Keywords

- Convex sets
- Rectangles
- Set systems
- Weak epsilon-nets

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

Aronov, B., Aurenhammer, F., Hurtado, F., Langerman, S., Rappaport, D., Seara, C., & Smorodinsky, S. (2009). Small weak epsilon-nets.

*Computational Geometry: Theory and Applications*,*42*(5), 455-462. https://doi.org/10.1016/j.comgeo.2008.02.005