{"paper":{"title":"On finding exact solutions of linear programs in the oracle model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.OC","authors_text":"Daniel Dadush, Giacomo Zambelli, L\\'aszl\\'o A. V\\'egh","submitted_at":"2026-06-10T08:54:38Z","abstract_excerpt":"We consider linear programming in the oracle model: $\\max\\{c^\\top x \\,:\\, x\\in P\\}$, where the polyhedron $P=\\{x\\in\\mathbb{R}^n\\,:\\, Ax\\le b\\}$ is given by a separation oracle. We present an algorithm that finds exact primal and dual solutions using $O(n^2\\log(n/\\delta))$ oracle calls and $O(n^4\\log(n/\\delta)+n^5\\log\\log(1/\\delta))$ arithmetic operations, where $\\delta$ is a geometric condition number associated with the system $(A,b)$. These bounds do not depend on the cost vector $c$ and do not require a priori knowledge of $\\delta$. For rational data, $\\log(1/\\delta)$ is polynomially bounde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11820","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/2606.11820/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"}