{"paper":{"title":"Approximate Generalized Matching: $f$-Factors and $f$-Edge Covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dawei Huang, Seth Pettie","submitted_at":"2017-06-19T01:36:58Z","abstract_excerpt":"In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\\epsilon(m)$-time algorithms for $(1-\\epsilon)$-maximum weight $f$-factor and $(1+\\epsilon)$-approximate minimum weight $f$-edge cover. As a byproduct, we also obtain direct algorithms for the exact cardinality versions of these problems running in $O(m\\sqrt{f(V)})$ time.\n  The technical contributions of this work include an efficient method for maintaining {\\em relaxed complementary slackness} in generalized matching problems and approximation-pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05761","kind":"arxiv","version":3},"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/1706.05761/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"}