Article

A data structure for multi-dimensional range reporting

Author:

Yakov NekrichAuthors Info & Claims

SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry

Pages 344 - 353

https://doi.org/10.1145/1247069.1247130

Published: 06 June 2007 Publication History

Abstract

We present a static data structure for orthogonal range reporting on a U x U x U integer grid. Our data structure supports orthogonal range reporting queries in O((log log n)² + log log U + k) time and uses O(n log⁴ n) space, where k is the size of the answer. We describe a static data structure for range reporting in R⁴ with O(log nlog log n +k) query time and a static data structure for range reporting in R^d, d ≥ 5, with query time O((log^d-3 n)/(log log n)^d-5 +k). We also describe a semi-dynamic data structure that supports range reporting queries in R³ in O(log nlog log n +k) time and insertions in polylogarithmic time.

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Cited By

Nekrich YMarx D(2021)New data structures for orthogonal range reporting and range minima queriesProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458137(1191-1205)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458137
Chan TNekrich YSmid M(2019)Orthogonal Range Reporting and Rectangle Stabbing for Fat RectanglesAlgorithms and Data Structures10.1007/978-3-030-24766-9_21(283-295)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-24766-9_21
Afshani PTsakalidis K(2018)Optimal Deterministic Shallow Cuttings for 3-d Dominance RangesAlgorithmica10.1007/s00453-017-0376-380:11(3192-3206)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s00453-017-0376-3
Show More Cited By

Index Terms

A data structure for multi-dimensional range reporting
1. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Sorting and searching

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cover image ACM Conferences

SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry

June 2007

404 pages

ISBN:9781595937056

DOI:10.1145/1247069

Program Chair:
Jeff Erickson
University of Illinois, Urbana-Champaign, USA

Copyright © 2007 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 June 2007

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

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Cited By

Nekrich YMarx D(2021)New data structures for orthogonal range reporting and range minima queriesProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458137(1191-1205)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458137
Chan TNekrich YSmid M(2019)Orthogonal Range Reporting and Rectangle Stabbing for Fat RectanglesAlgorithms and Data Structures10.1007/978-3-030-24766-9_21(283-295)Online publication date: 12-Jul-2019
https://doi.org/10.1007/978-3-030-24766-9_21
Afshani PTsakalidis K(2018)Optimal Deterministic Shallow Cuttings for 3-d Dominance RangesAlgorithmica10.1007/s00453-017-0376-380:11(3192-3206)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s00453-017-0376-3
Afshani PTsakalidis KChekuri C(2014)Optimal deterministic shallow cuttings for 3D dominance rangesProceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/2634074.2634176(1389-1398)Online publication date: 5-Jan-2014
https://dl.acm.org/doi/10.5555/2634074.2634176
Chan T(2013)Persistent Predecessor Search and Orthogonal Point Location on the Word RAMACM Transactions on Algorithms10.1145/2483699.24837029:3(1-22)Online publication date: 1-Jun-2013
https://dl.acm.org/doi/10.1145/2483699.2483702
Chan TRandall D(2011)Persistent predecessor search and orthogonal point location on the word RAMProceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms10.5555/2133036.2133121(1131-1145)Online publication date: 23-Jan-2011
https://dl.acm.org/doi/10.5555/2133036.2133121
Chan TLarsen KPătraşcu MHurtado Fvan Kreveld M(2011)Orthogonal range searching on the RAM, revisitedProceedings of the twenty-seventh annual symposium on Computational geometry10.1145/1998196.1998198(1-10)Online publication date: 13-Jun-2011
https://dl.acm.org/doi/10.1145/1998196.1998198
Nekrich Y(2010)Dynamic Range Reporting in External MemoryAlgorithms and Computation10.1007/978-3-642-17514-5_3(25-36)Online publication date: 2010
https://doi.org/10.1007/978-3-642-17514-5_3
Afshani PArge LLarsen K(2009)Orthogonal Range Reporting in Three and Higher DimensionsProceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science10.1109/FOCS.2009.58(149-158)Online publication date: 25-Oct-2009
https://dl.acm.org/doi/10.1109/FOCS.2009.58
Nekrich Y(2009)Data Structures for Approximate Orthogonal Range CountingProceedings of the 20th International Symposium on Algorithms and Computation10.1007/978-3-642-10631-6_20(183-192)Online publication date: 5-Dec-2009
https://dl.acm.org/doi/10.1007/978-3-642-10631-6_20
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