{"paper":{"title":"A Combinatorial $\\tilde{O}(m^{3/2})$-time Algorithm for the Min-Cost Flow Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andreas Karrenbauer, Ruben Becker","submitted_at":"2013-12-13T19:01:48Z","abstract_excerpt":"We present a combinatorial method for the min-cost flow problem and prove that its expected running time is bounded by $\\tilde O(m^{3/2})$. This matches the best known bounds, which previously have only been achieved by numerical algorithms or for special cases. Our contribution contains three parts that might be interesting in their own right: (1) We provide a construction of an equivalent auxiliary network and interior primal and dual points with potential $P_0=\\tilde{O}(\\sqrt{m})$ in linear time. (2) We present a combinatorial potential reduction algorithm that transforms initial solutions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3905","kind":"arxiv","version":2},"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"}