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arXiv · 0901.1761

Towards Optimal Range Medians

Beat Gfeller·Peter Sanders
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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 $O(n\log k + k\log n)$ time to answer the first $k$ queries. This improves previous algorithms by a logarithmic factor and matches a lower bound for $k=O(n)$. Since 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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Beat Gfeller, Peter Sanders. 2009-01-13. Towards Optimal Range Medians. https://arxiv.org/abs/0901.1761

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