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Lower bounds for orthogonal range searching: part II. The arithmetic model

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Bernard ChazelleAuthors Info & Claims

Journal of the ACM (JACM), Volume 37, Issue 3

Pages 439 - 463

https://doi.org/10.1145/79147.79149

Published: 01 July 1990 Publication History

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Abstract

Lower bounds on the complexity of orthogonal range searching in the static case are established. Specifically, we consider the following dominance search problem: Given a collection of n weighted points in d-space and a query point q, compute the cumulative weight of the points dominated (in all coordinates) by q. It is assumed that the weights are chosen in a commutative semigroup and that the query time measures only the number of arithmetic operations needed to compute the answer. It is proved that if m units of storage are available, then the query time is at least proportional to (log n/log(2m/n))^d–*1 in both the worst and average cases. This lower bound is provably tight for m = Ω(n(log n)^d–1+ϵ) and any fixed ϵ > 0. A lower bound of Ω(n/log log n)^d) on the time required for executing n inserts and queries is also established. —Author's Abstract

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Lower bounds for orthogonal range searching: part II. The arithmetic model

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Reviewer: Patrick J. Ryan

This lengthy paper is difficult to read because many definitions and statements lack mathematical precision. Motivational remarks are mixed with rigorous statements in a confusing way. The presentation could have been improved by restricting the rigorous part to a single thread and including some explicit examples.

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Published In

Journal of the ACM Volume 37, Issue 3

July 1990

247 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/79147

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1990

Published in JACM Volume 37, Issue 3

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Lower bounds for 2-dimensional range counting

Orthogonal range searching on the RAM, revisited

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