Dynamic Range Selection in Linear Space

  • Meng He
  • J. Ian Munro
  • Patrick K. Nicholson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

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.

Keywords

Internal Node Matrix Structure Query Range Query Time Ranking Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Meng He
    • 1
  • J. Ian Munro
    • 2
  • Patrick K. Nicholson
    • 2
  1. 1.Faculty of Computer ScienceDalhousie UniversityCanada
  2. 2.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada

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