### Abstract

We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit allconvex objects containingmore than 4n/7 points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure forfinding small number of points hitting convex sets over P, yieldingseveral improvements over previous results.

Original language | English (US) |
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Title of host publication | Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07 |

Pages | 138-141 |

Number of pages | 4 |

DOIs | |

State | Published - Oct 22 2007 |

Event | 23rd Annual Symposium on Computational Geometry, SCG'07 - Gyeongju, Korea, Republic of Duration: Jun 6 2007 → Jun 8 2007 |

### Other

Other | 23rd Annual Symposium on Computational Geometry, SCG'07 |
---|---|

Country | Korea, Republic of |

City | Gyeongju |

Period | 6/6/07 → 6/8/07 |

### Fingerprint

### Keywords

- Centerpoint theorem
- Combinatorial geometry
- Discrete geometry
- Extremal methods
- Hitting convex sets
- Weak -nets

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07*(pp. 138-141) https://doi.org/10.1145/1247069.1247097

**An optimal generalization of the centerpoint theorem, and its extensions.** / Mustafa, Nabil; Ray, Saurabh.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07.*pp. 138-141, 23rd Annual Symposium on Computational Geometry, SCG'07, Gyeongju, Korea, Republic of, 6/6/07. https://doi.org/10.1145/1247069.1247097

}

TY - GEN

T1 - An optimal generalization of the centerpoint theorem, and its extensions

AU - Mustafa, Nabil

AU - Ray, Saurabh

PY - 2007/10/22

Y1 - 2007/10/22

N2 - We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit allconvex objects containingmore than 4n/7 points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure forfinding small number of points hitting convex sets over P, yieldingseveral improvements over previous results.

AB - We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit allconvex objects containingmore than 4n/7 points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure forfinding small number of points hitting convex sets over P, yieldingseveral improvements over previous results.

KW - Centerpoint theorem

KW - Combinatorial geometry

KW - Discrete geometry

KW - Extremal methods

KW - Hitting convex sets

KW - Weak -nets

UR - http://www.scopus.com/inward/record.url?scp=35348923507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35348923507&partnerID=8YFLogxK

U2 - 10.1145/1247069.1247097

DO - 10.1145/1247069.1247097

M3 - Conference contribution

AN - SCOPUS:35348923507

SN - 1595937056

SN - 9781595937056

SP - 138

EP - 141

BT - Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07

ER -