### Abstract

We give a lower bound on the following problem, known as simplex range reporting: Given a collection P of n points in d-space and an arbitrary simplex q, find all the points in P ∩ q. It is understood that P is fixed and can be preprocessed ahead of time, while q is a query that must be answered on-line. We consider data structures for this problem that can be modeled on a pointer machine and whose query time is bounded by O(n^{δ} + r), where r is the number of points to be reported and δ is an arbitrary fixed real. We prove that any such data structure of that form must occupy storage Ω(n^{d(1-δ)-ε}), for any fixed ε > 0. This lower bound is tight within a factor of n^{ε}.

Original language | English (US) |
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Pages (from-to) | 237-247 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 5 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1996 |

### 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

*Computational Geometry: Theory and Applications*,

*5*(5), 237-247. https://doi.org/10.1016/0925-7721(95)00002-X