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Linear-Space Data Structures for Range Minority Query in Arrays

  • Timothy M. Chan
  • Stephane Durocher
  • Matthew Skala
  • Bryan T. Wilkinson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

Abstract

We consider range queries in arrays that search for low-frequency elements: least frequent elements and α-minorities. An α-minority of a query range has multiplicity no greater than an α fraction of the elements in the range. Our data structure for the least frequent element range query problem requires O(n) space, O(n 3/2) preprocessing time, and \(O(\sqrt{n})\) query time. A reduction from boolean matrix multiplication to this problem shows the hardness of simultaneous improvements in both preprocessing time and query time. Our data structure for the α-minority range query problem requires O(n) space, supports queries in O(1/α) time, and allows α to be specified at query time.

Keywords

Distinct Element Range Query Query Time Minimum Frequency Horizontal Segment 
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 2012

Authors and Affiliations

  • Timothy M. Chan
    • 1
  • Stephane Durocher
    • 2
  • Matthew Skala
    • 2
  • Bryan T. Wilkinson
    • 1
  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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