Towards Optimal Range Medians

  • Beat Gfeller
  • Peter Sanders
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5555)

Abstract

We consider the following problem: given an unsorted array of n elements, and a sequence of intervals in the array, compute the median in each of the subarrays defined by the intervals. We describe a simple algorithm which uses O(n) space and needs O(nlogk + klogn) time to answer k such median queries. This improves previous algorithms by a logarithmic factor and matches a lower bound for k = O(n). Since, in contrast to previous approaches, the algorithm decomposes the range of element values rather than the array, it has natural generalizations to higher-dimensional problems – it reduces a range median query to a logarithmic number of range counting queries.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Beat Gfeller
    • 1
  • Peter Sanders
    • 2
  1. 1.ETH ZürichSwitzerland
  2. 2.Universität KarlsruheGermany

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