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.

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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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