{"paper":{"title":"Faster p-norm minimizing flows, via smoothed q-norm problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC"],"primary_cat":"cs.DS","authors_text":"Deeksha Adil, Sushant Sachdeva","submitted_at":"2019-10-23T14:12:50Z","abstract_excerpt":"We present faster high-accuracy algorithms for computing $\\ell_p$-norm minimizing flows. On a graph with $m$ edges, our algorithm can compute a $(1+1/\\text{poly}(m))$-approximate unweighted $\\ell_p$-norm minimizing flow with $pm^{1+\\frac{1}{p-1}+o(1)}$ operations, for any $p \\ge 2,$ giving the best bound for all $p\\gtrsim 5.24.$ Combined with the algorithm from the work of Adil et al. (SODA '19), we can now compute such flows for any $2\\le p\\le m^{o(1)}$ in time at most $O(m^{1.24}).$ In comparison, the previous best running time was $\\Omega(m^{1.33})$ for large constant $p.$ For $p\\sim\\delta^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.10571","kind":"arxiv","version":2},"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/1910.10571/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"}