{"paper":{"title":"Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg-Rao","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Richard Peng, Yang P. Liu, Yu Gao","submitted_at":"2021-01-18T18:38:34Z","abstract_excerpt":"We give an algorithm for computing exact maximum flows on graphs with $m$ edges and integer capacities in the range $[1, U]$ in $\\widetilde{O}(m^{\\frac{3}{2} - \\frac{1}{328}} \\log U)$ time. For sparse graphs with polynomially bounded integer capacities, this is the first improvement over the $\\widetilde{O}(m^{1.5} \\log U)$ time bound from [Goldberg-Rao JACM `98].\n  Our algorithm revolves around dynamically maintaining the augmenting electrical flows at the core of the interior point method based algorithm from [M\\k{a}dry JACM `16]. This entails designing data structures that, in limited settin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.07233","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/2101.07233/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"}