Optimal Quantile Estimation for Streams

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" summary

Describes a deterministic quantile sketch that achieves deterministic O(1/ε) words space, matching a new lower bound. Builds on Q-digest trees but processes the stream in alpha-sized batches and replaces one level with a smaller “inner Q-digest” (or recursive instances) to shrink the universe repeatedly, trading log factors into a log* U recursion. Shows design details, space accounting, and that the construction is implementable with a few recursion layers and is provably optimal.

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" chapters (9)

1. 0:00Quantile estimation in streams
2. 1:25Problem definition and applications
3. 3:33History of quantile sketches
4. 7:36Q-digest sketch analysis
5. 15:53Improving Q-digest with counts
6. 23:05Recursive inner Q-digest
7. 27:00Final algorithm and optimizations
8. 31:45Lower bounds and optimality
9. 33:17Practical considerations and Q&A