{"paper":{"title":"A Matrix Factorization Approach in Turnstile Streaming","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jan Bulanek, Jelani Nelson, Raghu Meka, Ravi Kumar, Tamas Sarlos","submitted_at":"2026-07-30T20:21:49Z","abstract_excerpt":"We define the $M$-point query problem in data streams. Given a fixed matrix $M$, the goal is to maintain a vector $x$ under turnstile updates and answer each query $u$ with an estimate $\\widehat{y}_u$ satisfying $|y_u-\\widehat{y}_u| \\leq \\varepsilon \\|x\\|_1$, where $y=Mx$. We show that if $M$ admits a factorization $M=AB$, where $A$ and $B$ have space-efficient representations, then there is a streaming algorithm using $O(\\varepsilon^{-1}\\|A\\|_{2\\rightarrow\\infty}\\|B\\|_{1\\rightarrow 1}+(\\varepsilon^{-1}\\|A\\|_{\\infty\\rightarrow\\infty}\\|B\\|_{1\\rightarrow 1})^{2/3})$ words of memory.\n  An importa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28819","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/2607.28819/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"}