{"paper":{"title":"Solving Linear Programs in the Current Matrix Multiplication Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael B. Cohen, Yin Tat Lee, Zhao Song","submitted_at":"2018-10-18T04:37:51Z","abstract_excerpt":"This paper shows how to solve linear programs of the form $\\min_{Ax=b,x\\geq0} c^\\top x$ with $n$ variables in time $$O^*((n^{\\omega}+n^{2.5-\\alpha/2}+n^{2+1/6}) \\log(n/\\delta))$$ where $\\omega$ is the exponent of matrix multiplication, $\\alpha$ is the dual exponent of matrix multiplication, and $\\delta$ is the relative accuracy. For the current value of $\\omega\\sim2.37$ and $\\alpha\\sim0.31$, our algorithm takes $O^*(n^{\\omega} \\log(n/\\delta))$ time. When $\\omega = 2$, our algorithm takes $O^*(n^{2+1/6} \\log(n/\\delta))$ time.\n  Our algorithm utilizes several new concepts that we believe may be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07896","kind":"arxiv","version":3},"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/1810.07896/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"}