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Dynamic Range Selection in Linear Space

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Algorithms and Computation (ISAAC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7074))

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Abstract

Given a set S of n points in the plane, we consider the problem of answering range selection queries on S: that is, given an arbitrary x-range Q and an integer k > 0, return the k-th smallest y-coordinate from the set of points that have x-coordinates in Q. We present a linear space data structure that maintains a dynamic set of n points in the plane with real coordinates, and supports range selection queries in \(O((\lg n / \lg \lg n)^2)\) time, as well as insertions and deletions in \(O((\lg n / \lg \lg n)^2)\) amortized time. The space usage of this data structure is an \(\Theta(\lg n / \lg \lg n)\) factor improvement over the previous best result, while maintaining asymptotically matching query and update times. We also present a succinct data structure that supports range selection queries on a dynamic array of n values drawn from a bounded universe.

This work was supported by NSERC and the Canada Research Chairs Program.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, Dalhousie University, Canada

    Meng He

  2. David R. Cheriton School of Computer Science, University of Waterloo, Canada

    J. Ian Munro & Patrick K. Nicholson

Authors
  1. Meng He
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  2. J. Ian Munro
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  3. Patrick K. Nicholson
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Editor information

Editors and Affiliations

  1. Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan

    Takao Asano

  2. Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

  3. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Yoshio Okamoto

  4. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Osamu Watanabe

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He, M., Munro, J.I., Nicholson, P.K. (2011). Dynamic Range Selection in Linear Space. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_18

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  • DOI: https://doi.org/10.1007/978-3-642-25591-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25590-8

  • Online ISBN: 978-3-642-25591-5

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