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arXiv · 0807.0222

Range Medians

Sariel Har-Peled·S. Muthukrishnan
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Abstract

We study a generalization of the classical median finding problem to batched query case: given an array of unsorted $n$ items and $k$ (not necessarily disjoint) intervals in the array, the goal is to determine the median in {\em each} of the intervals in the array. We give an algorithm that uses $O(n\log n + k\log k \log n)$ comparisons and show a lower bound of $Ω(n\log k)$ comparisons for this problem. This is optimal for $k=O(n/\log n)$.

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Sariel Har-Peled, S. Muthukrishnan. 2008-07-01. Range Medians. https://arxiv.org/abs/0807.0222

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