### 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) |
---|---|

Pages (from-to) | 455-462 |

Number of pages | 8 |

Journal | Computational Geometry: Theory and Applications |

Volume | 42 |

Issue number | 5 |

DOIs | |

State | Published - Jul 2009 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Computational Geometry: Theory and Applications*,

*42*(5), 455-462. https://doi.org/10.1016/j.comgeo.2008.02.005

**Small weak epsilon-nets.** / Aronov, Boris; Aurenhammer, Franz; Hurtado, Ferran; Langerman, Stefan; Rappaport, David; Seara, Carlos; Smorodinsky, Shakhar.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 42, no. 5, pp. 455-462. https://doi.org/10.1016/j.comgeo.2008.02.005

}

TY - JOUR

T1 - Small weak epsilon-nets

AU - Aronov, Boris

AU - Aurenhammer, Franz

AU - Hurtado, Ferran

AU - Langerman, Stefan

AU - Rappaport, David

AU - Seara, Carlos

AU - Smorodinsky, Shakhar

PY - 2009/7

Y1 - 2009/7

N2 - 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.

AB - 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.

KW - Convex sets

KW - Rectangles

KW - Set systems

KW - Weak epsilon-nets

UR - http://www.scopus.com/inward/record.url?scp=84867987234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867987234&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2008.02.005

DO - 10.1016/j.comgeo.2008.02.005

M3 - Article

VL - 42

SP - 455

EP - 462

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 5

ER -