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Colored Range Searching in Linear Space

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Algorithm Theory – SWAT 2014 (SWAT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8503))

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Abstract

In colored range searching, we are given a set of n colored points in d ≥ 2 dimensions to store, and want to support orthogonal range queries taking colors into account. In the colored range counting problem, a query must report the number of distinct colors found in the query range, while an answer to the colored range reporting problem must report the distinct colors in the query range.

We give the first linear space data structure for both problems in two dimensions (d = 2) with o(n) worst case query time. We also give the first data structure obtaining almost-linear space usage and o(n) worst case query time for points in d > 2 dimensions. Finally, we present the first dynamic solution to both counting and reporting with o(n) query time for d ≥ 2 and d ≥ 3 dimensions, respectively.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Italy

    Roberto Grossi

  2. Technical University of Denmark, DTU Compute, Denmark

    Søren Vind

Authors
  1. Roberto Grossi
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  2. Søren Vind
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Editor information

Editors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    R. Ravi

  2. DTU Informatics, 2800, Kongens Lyngby, Denmark

    Inge Li Gørtz

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Grossi, R., Vind, S. (2014). Colored Range Searching in Linear Space. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-08404-6_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08403-9

  • Online ISBN: 978-3-319-08404-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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