{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:26:28Z","timestamp":1787340388793,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>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. The development of the algorithm entails two subresults of independent interest: (i) A $(D+\\sqrt{n})\\cdot n^{o(1)}$-round distributed construction of a spanning tree of average stretch $n^{o(1)}$. (ii) A $(D+\\sqrt{n})\\cdot n^{o(1)}$-round distributed construction of an $n^{o(1)}$-congestion approximator consisting of the cuts induced by $O(\\log n)$ virtual trees. The distributed representation of the cut approximator allows for evaluation in $(D+\\sqrt{n})\\cdot n^{o(1)}$ rounds. All our algorithms make use of randomization and succeed with high probability.<\/jats:p>","DOI":"10.1137\/17m113277x","type":"journal-article","created":{"date-parts":[[2018,11,27]],"date-time":"2018-11-27T12:54:00Z","timestamp":1543323240000},"page":"2078-2117","source":"Crossref","is-referenced-by-count":15,"title":["Near-Optimal Distributed Maximum Flow"],"prefix":"10.1137","volume":"47","author":[{"given":"Mohsen","family":"Ghaffari","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Karrenbauer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabian","family":"Kuhn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Lenzen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boaz","family":"Patt-Shamir","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,11,27]]},"reference":[{"key":"atypb1","first-page":"781","author":"Abraham I.","year":"2008","journal-title":"Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), IEEE, Washington, DC"},{"key":"atypb2","unstructured":"R. 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Madry,\n                      Fast Approximation Algorithms for Cut-Based Problems in Undirected Graphs\n                      , preprint,https:\/\/arxiv.org\/abs\/1008.1975, 2010.","DOI":"10.1109\/FOCS.2010.30"},{"key":"atypb23","first-page":"213","author":"Marberg J. M.","year":"1987","journal-title":"PA"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"Y. Nesterov,\n                      Introductory Lectures on Convex Optimization\n                      , Appl. Optim. 87, Springer Science & Business Media, New York, 2004.","DOI":"10.1007\/978-1-4419-8853-9"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.10.032"},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"D. Peleg,\n                      Distributed Computing: A Locality-Sensitive Approach\n                      , Discrete Math. 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Peng,\n                      Approximate Undirected Maximum Flows in $O(m \\, {{polylog}}\\, (n))$ Time\n                      ,https:\/\/arxiv.org\/abs\/1411.7631, 2014."},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1287\/moor.20.2.257"},{"key":"atypb29","first-page":"255","author":"R\u00e4cke H.","year":"2008","journal-title":"New York"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100259"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230120302"},{"key":"atypb32","first-page":"263","author":"Sherman J.","year":"2013","journal-title":"Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), IEEE, Washington, DC"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.2001.959930"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M113277X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:32:38Z","timestamp":1787337158000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M113277X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":33,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M113277X"],"URL":"https:\/\/doi.org\/10.1137\/17m113277x","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}