{"paper":{"title":"Tight Bounds for Heavy-Hitters and Moment Estimation in the Sliding Window Model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Shiyuan Feng, William Swartworth","submitted_at":"2025-04-29T20:52:00Z","abstract_excerpt":"We consider the heavy-hitters and $F_p$ moment estimation problems in the sliding window model. For $F_p$ moment estimation with $1<p\\leq 2$, we show that it is possible to give a $(1\\pm \\epsilon)$ multiplicative approximation to the $F_p$ moment with $2/3$ probability on any given window of size $n$ using $\\tilde{O}(\\frac{1}{\\epsilon^p}\\log^2 n + \\frac{1}{\\epsilon^2}\\log n)$ 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 $\\log\\frac{1}{\\epsilon}.$ As a consequence of our $F_2$ moment estimation algorit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.21175","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.21175/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}