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Data Structures for Approximate Orthogonal Range Counting

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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Abstract

We present new data structures for approximately counting the number of points in an orthogonal range. There is a deterministic linear space data structure that supports updates in O(1) time and approximates the number of elements in a 1-D range up to an additive term k 1/c in O(loglogU·loglogn) time, where k is the number of elements in the answer, U is the size of the universe and c is an arbitrary fixed constant. We can estimate the number of points in a two-dimensional orthogonal range up to an additive term k ρ in O(loglogU + (1/ρ)loglogn) time for any ρ> 0. We can estimate the number of points in a three-dimensional orthogonal range up to an additive term k ρ in O(loglogU + (loglogn)3 + (3v)loglogn) time for \(v=\log \frac{1}{\rho}/\log \frac{3}{2}+2\).

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Bonn,  

    Yakov Nekrich

Authors
  1. Yakov Nekrich
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Nekrich, Y. (2009). Data Structures for Approximate Orthogonal Range Counting. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_20

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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