{"paper":{"title":"Minimum Cost Flow in the CONGEST Model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Tijn de Vos","submitted_at":"2023-04-04T07:41:41Z","abstract_excerpt":"We consider the CONGEST model on a network with $n$ nodes, $m$ edges, diameter $D$, and integer costs and capacities bounded by $\\text{poly} n$. In this paper, we show how to find an exact solution to the minimum cost flow problem in $n^{1/2+o(1)}(\\sqrt{n}+D)$ rounds, improving the state of the art algorithm with running time $m^{3/7+o(1)}(\\sqrt nD^{1/4}+D)$ [Forster et al. FOCS 2021], which only holds for the special case of unit capacity graphs. For certain graphs, we achieve even better results. In particular, for planar graphs, expander graphs, $n^{o(1)}$-genus graphs, $n^{o(1)}$-treewidth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.01600","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/2304.01600/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"}