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Tight Bounds for Heavy-Hitters and Moment Estimation in the Sliding Window Model

Authors Shiyuan Feng, William Swartworth, David Woodruff

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ACM Subject Classification
  • Theory of computation → Sketching and sampling
Keywords
  • sketching
  • streaming
  • heavy hitters
  • sliding window
  • moment estimation

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Abstract

We consider the heavy-hitters and F_p moment estimation problems in the sliding window model. For F_p moment estimation with 1 < p ≤ 2, we show that it is possible to give a (1± ε) multiplicative approximation to the F_p moment with 2/3 probability on any given window of size n using Õ(1/(ε^p)log² n + 1/(ε²)log n) bits of space. We complement this result with a lower bound showing that our algorithm gives tight bounds up to factors of log log n and log1/(ε). As a consequence of our F₂ moment estimation algorithm, we show that the heavy-hitters problem can be solved on an arbitrary window using O(1/(ε²)log² n) space which is tight.

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Shiyuan Feng, William Swartworth, and David Woodruff. Tight Bounds for Heavy-Hitters and Moment Estimation in the Sliding Window Model. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 75:1-75:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.75

Author Details

Shiyuan Feng
  • EECS, Peking University, Beijing, China
William Swartworth
  • Carnegie Mellon University, Pittsburgh, PA, USA
David Woodruff
  • Carnegie Mellon University, Pittsburgh, PA, USA

Funding

Authors William Swartworth and David Woodruff were supported by a Simons Investigator Award and Office of Naval Research award number N000142112647.

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