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Article

Lower bounds for intersection searching and fractional cascading in higher dimension

Authors:

Bernard Chazelle,

Ding LiuAuthors Info & Claims

STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

Pages 322 - 329

https://doi.org/10.1145/380752.380818

Published: 06 July 2001 Publication History

Abstract

Given an n-edge convex subdivision of the plane, is it possible to report its k intersections with a query line segment in O(k+$~polylog$(n)) time, using subquadratic storage? If the query is a plane and the input is a polytope with n vertices, can one achieve O(k+$~polylog$(n)) time with subcubic storage? Does any convex polytope have a boundary dominant Dobkin-Kirkpatrick hierarchy? Can fractional cascading be generalized to planar maps instead of linear lists? We prove that the answer to all of these questions is no, and we derive near-optimal solutions to these classical problems.

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Cited By

Lin A(2019)Binary search algorithmWikiJournal of Science10.15347/wjs/2019.0052:1(5)Online publication date: 2019
https://doi.org/10.15347/wjs/2019.005
Shi QJaJa J(2019)Optimal and near-optimal algorithms for generalized intersection reporting on pointer machinesInformation Processing Letters10.1016/j.ipl.2005.04.00895:3(382-388)Online publication date: 5-Jan-2019
https://dl.acm.org/doi/10.1016/j.ipl.2005.04.008
Larsen KNguyen HDey TWhitesides S(2012)Improved range searching lower boundsProceedings of the twenty-eighth annual symposium on Computational geometry10.1145/2261250.2261275(171-178)Online publication date: 17-Jun-2012
https://dl.acm.org/doi/10.1145/2261250.2261275

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Lower bounds for intersection searching and fractional cascading in higher dimension

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cover image ACM Conferences

STOC '01: Proceedings of the thirty-third annual ACM symposium on Theory of computing

July 2001

755 pages

ISBN:1581133499

DOI:10.1145/380752

Copyright © 2001 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 06 July 2001

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Cited By

Lin A(2019)Binary search algorithmWikiJournal of Science10.15347/wjs/2019.0052:1(5)Online publication date: 2019
https://doi.org/10.15347/wjs/2019.005
Shi QJaJa J(2019)Optimal and near-optimal algorithms for generalized intersection reporting on pointer machinesInformation Processing Letters10.1016/j.ipl.2005.04.00895:3(382-388)Online publication date: 5-Jan-2019
https://dl.acm.org/doi/10.1016/j.ipl.2005.04.008
Larsen KNguyen HDey TWhitesides S(2012)Improved range searching lower boundsProceedings of the twenty-eighth annual symposium on Computational geometry10.1145/2261250.2261275(171-178)Online publication date: 17-Jun-2012
https://dl.acm.org/doi/10.1145/2261250.2261275

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