Article

Space efficient dynamic orthogonal range reporting

Author:

Yakov NekrichAuthors Info & Claims

SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

Pages 306 - 313

https://doi.org/10.1145/1064092.1064139

Published: 06 June 2005 Publication History

Abstract

In this paper we present new space e cient dynamic data structures for orthogonal range reporting.The described data structures support planar range reporting queries in time O (log n +k log log(4 n/(k +1)))and space O (n log log n ), or in time O (log n+k )and space O (n log e n )for any e > 0. Both data structures can be constructed in O (n log n )time and support insert and delete operations in amortized time O (log 2 n )and O (log n log log n )respectively. These results match the corresponding upper space bounds of Chazelle [6] for the static case. We also present a dynamic data structure for d -dimensional range reporting with search time O (log d .1 n +k ),update time O (log d n ),and space O (n log d .2+e n )for any e > 0.

References

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Cited By

Farzan AGagie TNavarro G(2010)Entropy-Bounded Representation of Point GridsAlgorithms and Computation10.1007/978-3-642-17514-5_28(327-338)Online publication date: 2010
https://doi.org/10.1007/978-3-642-17514-5_28
Nekrich Y(2009)Orthogonal range searching in linear and almost-linear spaceComputational Geometry: Theory and Applications10.1016/j.comgeo.2008.09.00142:4(342-351)Online publication date: 1-May-2009
https://dl.acm.org/doi/10.1016/j.comgeo.2008.09.001
Blelloch GTeng S(2008)Space-efficient dynamic orthogonal point location, segment intersection, and range reportingProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347180(894-903)Online publication date: 20-Jan-2008
https://dl.acm.org/doi/10.5555/1347082.1347180
Show More Cited By

Index Terms

Space efficient dynamic orthogonal range reporting
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

June 2005

398 pages

ISBN:1581139918

DOI:10.1145/1064092

Program Chairs:
Joe Mitchell
SUNY Stony Brook
,
Günter Rote
Freie Universität Berlin

Copyright © 2005 ACM.

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Published: 06 June 2005

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SoCG05: The 21st Annual ACM Symposium on Computational Geometry 2005

June 6 - 8, 2005

Pisa, Italy

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SCG '05 Paper Acceptance Rate 41 of 141 submissions, 29%;

Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Farzan AGagie TNavarro G(2010)Entropy-Bounded Representation of Point GridsAlgorithms and Computation10.1007/978-3-642-17514-5_28(327-338)Online publication date: 2010
https://doi.org/10.1007/978-3-642-17514-5_28
Nekrich Y(2009)Orthogonal range searching in linear and almost-linear spaceComputational Geometry: Theory and Applications10.1016/j.comgeo.2008.09.00142:4(342-351)Online publication date: 1-May-2009
https://dl.acm.org/doi/10.1016/j.comgeo.2008.09.001
Blelloch GTeng S(2008)Space-efficient dynamic orthogonal point location, segment intersection, and range reportingProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347180(894-903)Online publication date: 20-Jan-2008
https://dl.acm.org/doi/10.5555/1347082.1347180
Nekrich Y(2007)Orthogonal range searching in linear and almost-linear spaceProceedings of the 10th international conference on Algorithms and Data Structures10.5555/2394893.2394898(15-26)Online publication date: 15-Aug-2007
https://dl.acm.org/doi/10.5555/2394893.2394898
Nekrich YErickson J(2007)A data structure for multi-dimensional range reportingProceedings of the twenty-third annual symposium on Computational geometry10.1145/1247069.1247130(344-353)Online publication date: 6-Jun-2007
https://dl.acm.org/doi/10.1145/1247069.1247130
Nekrich Y(2007)Orthogonal Range Searching in Linear and Almost-Linear SpaceAlgorithms and Data Structures10.1007/978-3-540-73951-7_3(15-26)Online publication date: 2007
https://doi.org/10.1007/978-3-540-73951-7_3

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