{"paper":{"title":"Streaming Semidefinite Programs: $O(\\sqrt{n})$ Passes, Small Space and Fast Runtime","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lichen Zhang, Mingquan Ye, Zhao Song","submitted_at":"2023-09-10T21:07:19Z","abstract_excerpt":"We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, $m$ constraint matrices and a target matrix $C$, all of size $n\\times n$ together with a vector $b\\in \\mathbb{R}^m$ are streamed to us one-by-one. The goal is to find a matrix $X\\in \\mathbb{R}^{n\\times n}$ such that $\\langle C, X\\rangle$ is maximized, subject to $\\langle A_i, X\\rangle=b_i$ for all $i\\in [m]$ and $X\\succeq 0$. Previous algorithmic studies of SDP primarily focus on \\emph{time-efficiency}, and all of them require a prohibitively large $\\Omega(mn^2)$ space in order to store \\emph{all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05135","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/2309.05135/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"}