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Range searching with efficient hierarchical cuttings

Author:

Jiří MatoušekAuthors Info & Claims

Discrete & Computational Geometry, Volume 10, Issue 2

Pages 157 - 182

https://doi.org/10.1007/BF02573972

Published: 01 December 1993 Publication History

Abstract

We present an improved space/query-time tradeoff for the general simplex range searching problem, matching known lower bounds up to small polylogarithmic factors. In particular, we construct a linear-space simplex range searching data structure withO(n1 1/d) query time, which is optimal ford=2 and probably also ford>2. Further, we show that multilevel range searching data structures can be built with only a polylogarithmic overhead in space and query time per level (the previous solutions require at least a small fixed power ofn). We show that Hopcroft's problem (detecting an incidence amongn lines andn points) can be solved in time $$n^{4/3} 2^{O(\log ^4 n)}$$ . In all these algorithms we apply Chazelle's results on computing optimal cuttings.

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Chan TZheng D(2024)Hopcroft’s Problem, Log* Shaving, Two-dimensional Fractional Cascading, and Decision TreesACM Transactions on Algorithms10.1145/359135720:3(1-27)Online publication date: 21-Jun-2024
https://dl.acm.org/doi/10.1145/3591357
Afshani PCheng P(2024)On Semialgebraic Range ReportingDiscrete & Computational Geometry10.1007/s00454-023-00574-171:1(4-39)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s00454-023-00574-1
Ahn TChung CAhn HBae SCheong OYoon S(2024)Minimum-Width Double-Slabs and Widest Empty Slabs in High DimensionsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_20(303-317)Online publication date: 18-Mar-2024
https://dl.acm.org/doi/10.1007/978-3-031-55598-5_20
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Range searching with efficient hierarchical cuttings
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
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cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 10, Issue 2

August 1993

118 pages

ISSN:0179-5376

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1993

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Cited By

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Chan TZheng D(2024)Hopcroft’s Problem, Log* Shaving, Two-dimensional Fractional Cascading, and Decision TreesACM Transactions on Algorithms10.1145/359135720:3(1-27)Online publication date: 21-Jun-2024
https://dl.acm.org/doi/10.1145/3591357
Afshani PCheng P(2024)On Semialgebraic Range ReportingDiscrete & Computational Geometry10.1007/s00454-023-00574-171:1(4-39)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s00454-023-00574-1
Ahn TChung CAhn HBae SCheong OYoon S(2024)Minimum-Width Double-Slabs and Widest Empty Slabs in High DimensionsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_20(303-317)Online publication date: 18-Mar-2024
https://dl.acm.org/doi/10.1007/978-3-031-55598-5_20
Afshani PCheng P(2023)Lower Bounds for Semialgebraic Range Searching and Stabbing ProblemsJournal of the ACM10.1145/357857470:2(1-26)Online publication date: 18-Apr-2023
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Chan TMarx D(2021)Near-optimal randomized algorithms for selection in totally monotone matricesProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458153(1483-1495)Online publication date: 10-Jan-2021
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Friedman RShahout RMargara AValle E(2021)Box queries over multi-dimensional streamsProceedings of the 15th ACM International Conference on Distributed and Event-based Systems10.1145/3465480.3466925(90-101)Online publication date: 28-Jun-2021
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de Berg M(2021)Removing Depth-Order Cycles Among Triangles: An Algorithm Generating Triangular FragmentsDiscrete & Computational Geometry10.1007/s00454-019-00102-065:2(450-469)Online publication date: 1-Mar-2021
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Mantas ISavić MSchrezenmaier H(2021)New Variants of Perfect Non-crossing MatchingsAlgorithms and Discrete Applied Mathematics10.1007/978-3-030-67899-9_12(151-164)Online publication date: 11-Feb-2021
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Berg MBuchin KJansen BWoeginger G(2020)Fine-grained Complexity Analysis of Two Classic TSP VariantsACM Transactions on Algorithms10.1145/341484517:1(1-29)Online publication date: 31-Dec-2020
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