### Abstract

The Centerpoint Theorem states that, for any set S of n points in R ^{d}, there exists a point p in R ^{d} such that every closed halfspace containing p contains at least [n/(d + 1)] points of S. We consider generalizations of the Centerpoint Theorem in which halfspaces are replaced with wedges (cones) of angle a. In M ^{2}, we give bounds that are tight for all values of a and give an O(n) time algorithm to find a point satisfying these bounds. We also give partial results for R ^{3} and, more generally, R ^{d}.

Original language | English (US) |
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Pages (from-to) | 45-54 |

Number of pages | 10 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 11 |

Issue number | 1 |

State | Published - Jul 27 2009 |

### Keywords

- Centerpoint
- Halfspace depth
- Wedges

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)
- Discrete Mathematics and Combinatorics

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## Cite this

Erickson, J., Hurtado, F., & Morin, P. (2009). Centerpoint theorems for wedges.

*Discrete Mathematics and Theoretical Computer Science*,*11*(1), 45-54.