## Abstract

In this paper we prove several point selection theorems concerning objects 'spanned' by a finite set of points. For example, we show that for any set P of n points in ℝ^{2} and any set C of m ≥4n distinct pseudo-circles, each passing through a distinct pair of points of P, there is a point in P that is covered by (i.e., lies in the interior of) Ω(m ^{2}/n^{2}) pseudo-circles of C. Similar problems involving point sets in higher dimensions are also studied. Most of our bounds are asymptotically tight, and they improve and generalize results of Chazelle, Edelsbrunner, Guibas, Hershberger, Seidel and Sharir, where weaker bounds for some of these cases were obtained.

Original language | English |
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Pages (from-to) | 389-411 |

Number of pages | 23 |

Journal | Combinatorics Probability and Computing |

Volume | 13 |

Issue number | 3 |

DOIs | |

State | Published - 1 May 2004 |

Externally published | Yes |

## ASJC Scopus subject areas

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