### 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^{ε}+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 Π(n^{d}(^{l-δ)-e}), for any fixed epsi > 0. This lower bound is tight within a factor of n^{ε}.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 19th International Colloquium, Proceedings |

Editors | Werner Kuich |

Publisher | Springer Verlag |

Pages | 439-449 |

Number of pages | 11 |

ISBN (Print) | 9783540557197 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

Event | 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992 - Wien, Austria Duration: Jul 13 1992 → Jul 17 1992 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 623 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992 |
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Country | Austria |

City | Wien |

Period | 7/13/92 → 7/17/92 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Automata, Languages and Programming - 19th International Colloquium, Proceedings*(pp. 439-449). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 623 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-55719-9_95

**Lower bounds on the complexity of simplex range reporting on a pointer machine.** / Chazelle, Bernard; Rosenberg, Burton J.

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

*Automata, Languages and Programming - 19th International Colloquium, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 623 LNCS, Springer Verlag, pp. 439-449, 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992, Wien, Austria, 7/13/92. https://doi.org/10.1007/3-540-55719-9_95

}

TY - GEN

T1 - Lower bounds on the complexity of simplex range reporting on a pointer machine

AU - Chazelle, Bernard

AU - Rosenberg, Burton J

PY - 1992/1/1

Y1 - 1992/1/1

N2 - 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(nε+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 Π(nd(l-δ)-e), for any fixed epsi > 0. This lower bound is tight within a factor of nε.

AB - 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(nε+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 Π(nd(l-δ)-e), for any fixed epsi > 0. This lower bound is tight within a factor of nε.

UR - http://www.scopus.com/inward/record.url?scp=84976668911&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976668911&partnerID=8YFLogxK

U2 - 10.1007/3-540-55719-9_95

DO - 10.1007/3-540-55719-9_95

M3 - Conference contribution

AN - SCOPUS:84976668911

SN - 9783540557197

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 439

EP - 449

BT - Automata, Languages and Programming - 19th International Colloquium, Proceedings

A2 - Kuich, Werner

PB - Springer Verlag

ER -