Quasi-optimal upper bounds for simplex range searching and new zone theorems

Bernard Chazelle; Micha Sharir; Emo Welzl

doi:10.1145/98524.98532

Quasi-optimal upper bounds for simplex range searching and new zone theorems

Bernard Chazelle^*, Micha Sharir, Emo Welzl

^*Corresponding author for this work

Princeton University

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

22 Scopus citations

Abstract

We consider the following problem, known as simplex range searching: Preprocess a set P of n points in R^d so that, given any query simplex q, the points in P intersection q can be counted or reported efficiently. We can put the many variants of this problem under the same umbrella by assuming a weight function on the points and asking for the cumulative weight of the points in P intersection q. For the sake of generality, it is best to disallow the use of subtraction (which will make our upper bounds more powerful): formally, this means choosing weights in an additive semigroup. The main topics are simplex range searching in polylogarithmic time, trading off storage and query time, and an improved theorem for planes in three dimensions.

Original language	English
Title of host publication	Proc Sixth Annu Symp Comput Geom
Publisher	Association for Computing Machinery (ACM)
Pages	23-33
Number of pages	11
ISBN (Print)	0897913620, 9780897913621
DOIs	https://doi.org/10.1145/98524.98532
State	Published - 1990
Externally published	Yes
Event	Proceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA Duration: 6 Jun 1990 → 8 Jun 1990

Publication series

Name	Proc Sixth Annu Symp Comput Geom

Conference

Conference	Proceedings of the Sixth Annual Symposium on Computational Geometry
City	Berkeley, CA, USA
Period	6/06/90 → 8/06/90

Access to Document

10.1145/98524.98532

Cite this

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title = "Quasi-optimal upper bounds for simplex range searching and new zone theorems",

abstract = "We consider the following problem, known as simplex range searching: Preprocess a set P of n points in Rd so that, given any query simplex q, the points in P intersection q can be counted or reported efficiently. We can put the many variants of this problem under the same umbrella by assuming a weight function on the points and asking for the cumulative weight of the points in P intersection q. For the sake of generality, it is best to disallow the use of subtraction (which will make our upper bounds more powerful): formally, this means choosing weights in an additive semigroup. The main topics are simplex range searching in polylogarithmic time, trading off storage and query time, and an improved theorem for planes in three dimensions.",

author = "Bernard Chazelle and Micha Sharir and Emo Welzl",

year = "1990",

doi = "10.1145/98524.98532",

language = "אנגלית",

isbn = "0897913620",

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publisher = "Association for Computing Machinery (ACM)",

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note = "Proceedings of the Sixth Annual Symposium on Computational Geometry ; Conference date: 06-06-1990 Through 08-06-1990",

}

Chazelle, B, Sharir, M & Welzl, E 1990, Quasi-optimal upper bounds for simplex range searching and new zone theorems. in Proc Sixth Annu Symp Comput Geom. Proc Sixth Annu Symp Comput Geom, Association for Computing Machinery (ACM), pp. 23-33, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/06/90. https://doi.org/10.1145/98524.98532

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AB - We consider the following problem, known as simplex range searching: Preprocess a set P of n points in Rd so that, given any query simplex q, the points in P intersection q can be counted or reported efficiently. We can put the many variants of this problem under the same umbrella by assuming a weight function on the points and asking for the cumulative weight of the points in P intersection q. For the sake of generality, it is best to disallow the use of subtraction (which will make our upper bounds more powerful): formally, this means choosing weights in an additive semigroup. The main topics are simplex range searching in polylogarithmic time, trading off storage and query time, and an improved theorem for planes in three dimensions.

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Quasi-optimal upper bounds for simplex range searching and new zone theorems

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