{"paper":{"title":"Scaling algorithms for approximate and exact maximum weight matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hsin-Hao Su, Ran Duan, Seth Pettie","submitted_at":"2011-12-04T20:05:24Z","abstract_excerpt":"The {\\em maximum cardinality} and {\\em maximum weight matching} problems can be solved in time $\\tilde{O}(m\\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and vertices.) In this article we demonstrate that this \"$m\\sqrt{n}$ barrier\" is extremely fragile, in the following sense. For any $\\epsilon>0$, we give an algorithm that computes a $(1-\\epsilon)$-approximate maximum weight matching in $O(m\\epsilon^{-1}\\log\\epsilon^{-1})$ time, that is, optimal {\\em linear time} for any fixed $\\epsilon$. Our algorithm is dramatically s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0790","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"}