{"paper":{"title":"Towards Optimal Moment Estimation in Streaming and Distributed Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Rajesh Jayaram","submitted_at":"2019-07-12T16:10:46Z","abstract_excerpt":"One of the oldest problems in the data stream model is to approximate the $p$-th moment $\\|\\mathcal{X}\\|_p^p = \\sum_{i=1}^n |\\mathcal{X}_i|^p$ of an underlying vector $\\mathcal{X} \\in \\mathbb{R}^n$, which is presented as a sequence of poly$(n)$ updates to its coordinates. Of particular interest is when $p \\in (0,2]$. Although a tight space bound of $\\Theta(\\epsilon^{-2} \\log n)$ bits is known for this problem when both positive and negative updates are allowed, surprisingly there is still a gap in the space complexity when all updates are positive. Specifically, the upper bound is $O(\\epsilon^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05816","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":""},"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"}