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How to show that the median cannot be maintained in $O(1)$ time?

If you can maintain the median of $n$ objects in $O(1)$, then you can sort a sequence $x_1, \dots, x_n$ in $O(n)$: first you compute a value $a$ smaller than all elements in the sequence and a value $...
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1 vote
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Single-pass streaming quantile estimation using moments

Gan et al. address this in Moment-Based Quantile Sketches for Efficient High Cardinality Aggregation Queries. The answers are rather nuanced.
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  • 11k

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