{"paper":{"title":"Flows in Almost Linear Time via Adaptive Preconditioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Di Wang, Rasmus Kyng, Richard Peng, Sushant Sachdeva","submitted_at":"2019-06-25T06:34:40Z","abstract_excerpt":"We present algorithms for solving a large class of flow and regression problems on unit weighted graphs to $(1 + 1 / poly(n))$ accuracy in almost-linear time. These problems include $\\ell_p$-norm minimizing flow for $p$ large ($p \\in [\\omega(1), o(\\log^{2/3} n) ]$), and their duals, $\\ell_p$-norm semi-supervised learning for $p$ close to $1$.\n  As $p$ tends to infinity, $\\ell_p$-norm flow and its dual tend to max-flow and min-cut respectively. Using this connection and our algorithms, we give an alternate approach for approximating undirected max-flow, and the first almost-linear time approxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10340","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"}