{"paper":{"title":"Lower Bounds for Approximating the Matching Polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Makrand Sinha","submitted_at":"2017-11-28T06:41:18Z","abstract_excerpt":"We prove that any extended formulation that approximates the matching polytope on $n$-vertex graphs up to a factor of $(1+\\varepsilon)$ for any $\\frac2n \\le \\varepsilon \\le 1$ must have at least $\\binom{n}{{\\alpha}/{\\varepsilon}}$ defining inequalities where $0<\\alpha<1$ is an absolute constant. This is tight as exhibited by the $(1+\\varepsilon)$ approximating linear program obtained by dropping the odd set constraints of size larger than $({1+\\varepsilon})/{\\varepsilon}$ from the description of the matching polytope. Previously, a tight lower bound of $2^{\\Omega(n)}$ was only known for $\\vare"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10145","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":""},"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"}