{"paper":{"title":"A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.NA","math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Sam Chiu-wai Wong, Yin Tat Lee","submitted_at":"2015-08-20T04:44:51Z","abstract_excerpt":"We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\\subset \\mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a point in $K$ or prove that $K$ does not contain a ball of radius $\\epsilon$ using an expected $O(n\\log(nR/\\epsilon))$ oracle evaluations and additional time $O(n^3\\log^{O(1)}(nR/\\epsilon))$. This matches the oracle complexity and improves upon the $O(n^{\\omega+1}\\log(nR/\\epsilon))$ additional time of the previous fastest algorithm achieved over 25 years ago"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04874","kind":"arxiv","version":2},"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"}