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)


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(n3/2) 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.


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© 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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