{"paper":{"title":"Computing Maximum Flow with Augmenting Electrical Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aleksander Madry","submitted_at":"2016-08-21T23:53:22Z","abstract_excerpt":"We present an $\\tilde{O}\\left(m^{\\frac{10}{7}}U^{\\frac{1}{7}}\\right)$-time algorithm for the maximum $s$-$t$ flow problem and the minimum $s$-$t$ cut problem in directed graphs with $m$ arcs and largest integer capacity $U$. This matches the running time of the $\\tilde{O}\\left((mU)^{\\frac{10}{7}}\\right)$-time algorithm of M\\k{a}dry (FOCS 2013) in the unit-capacity case, and improves over it, as well as over the $\\tilde{O}\\left(m \\sqrt{n} \\log U\\right)$-time algorithm of Lee and Sidford (FOCS 2014), whenever $U$ is moderately large and the graph is sufficiently sparse. By well-known reductions,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06016","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"}