{"paper":{"title":"Near-Optimal Distributed Maximum Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Andreas Karrenbauer, Boaz Patt-Shamir, Christoph Lenzen, Fabian Kuhn, Mohsen Ghaffari","submitted_at":"2015-08-19T19:17:55Z","abstract_excerpt":"We present a near-optimal distributed algorithm for $(1+o(1))$-approximation of single-commodity maximum flow in undirected weighted networks that runs in $(D+ \\sqrt{n})\\cdot n^{o(1)}$ communication rounds in the \\Congest model. Here, $n$ and $D$ denote the number of nodes and the network diameter, respectively. This is the first improvement over the trivial bound of $O(n^2)$, and it nearly matches the $\\tilde{\\Omega}(D+ \\sqrt{n})$ round complexity lower bound.\n  The development of the algorithm contains two results of independent interest:\n  (i) A $(D+\\sqrt{n})\\cdot n^{o(1)}$-round distribute"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04747","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"}