{"paper":{"title":"Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aleksander Madry","submitted_at":"2013-07-08T19:13:00Z","abstract_excerpt":"We present an $\\tilde{O}(m^{10/7})=\\tilde{O}(m^{1.43})$-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the long-standing $O(m \\min(\\sqrt{m},n^{2/3}))$ time bound due to Even and Tarjan [EvenT75]. By well-known reductions, this also establishes an $\\tilde{O}(m^{10/7})$-time algorithm for the maximum-cardinality bipartite matching problem. That, in turn, gives an improvement over the celebrated celebrated $O(m \\sqrt{n})$ time bound of Hopcroft and Karp [HK73] whenever th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2205","kind":"arxiv","version":3},"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"}