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Linear-Space Data Structures for Range Minority Query in Arrays

  • Conference paper
Algorithm Theory – SWAT 2012 (SWAT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7357))

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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.

Work supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Author information

Authors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Timothy M. Chan & Bryan T. Wilkinson

  2. Department of Computer Science, University of Manitoba, Winnipeg, Canada

    Stephane Durocher & Matthew Skala

Authors
  1. Timothy M. Chan
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  2. Stephane Durocher
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  3. Matthew Skala
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  4. Bryan T. Wilkinson
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Editor information

Editors and Affiliations

  1. Institute of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Department of Information and Computer Science, Aalto University, PO Box 15400, 00076, Aalto, Finland

    Petteri Kaski

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Chan, T.M., Durocher, S., Skala, M., Wilkinson, B.T. (2012). Linear-Space Data Structures for Range Minority Query in Arrays. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-31155-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31154-3

  • Online ISBN: 978-3-642-31155-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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