{"paper":{"title":"Polyhedral extended formulations that approximate the Gomory closure for packing problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Friedrich Eisenbrand, Jiaye Wei, Lars Rohwedder, Samuel Fiorini","submitted_at":"2026-07-10T09:13:00Z","abstract_excerpt":"We consider $0/1$ packing problems $\\max\\{c^T x \\colon Ax \\leq 1, \\, x \\in \\{0,1\\}^n\\}$, with $A \\in \\mathbb{R}_{\\geq 0}^{m \\times n}$. A way to solve such problems is via tightening the linear programming relaxation $P$ with Gomory \\emph{cutting-planes}. The Gomory-closure $P'$ of $P$ is the intersection of $P$ with all its cutting planes. The optimization problem over $P'$ is NP-hard. Mastrolilli (2020) has shown that for fixed ${\\epsilon}>0$, the Lasserre hierarchy yields a polynomial-size convex but non-polyhedral extended formulation that approximates $P'$ up to a factor of $1+{\\epsilon}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09222","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/2607.09222/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"}