{"paper":{"title":"Algebraic Algorithms for b-Matching, Shortest Undirected Paths, and f-Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Harold N. Gabow, Piotr Sankowski","submitted_at":"2013-04-24T20:26:13Z","abstract_excerpt":"Let G=(V,E) be a graph with f:V\\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \\tilde{O}(f(V)^{\\omega}). More generally for graphs with integral edge weights of maximum absolute value W we find a maximum weight f-factor in time \\tilde{O}(Wf(V)^{\\omega}). (The algorithms are randomized, correct with high probability and Las Vegas; the time bound is worst-case.) We also present three specializations of these algorithms: For maximum weight perfect f-matching the algorithm is considerably simpler (and almos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6740","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"}