{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EC3GXZTQQ5JI7NTXBZLD4SFD2G","short_pith_number":"pith:EC3GXZTQ","schema_version":"1.0","canonical_sha256":"20b66be67087528fb6770e563e48a3d1b1e90fad853fd8fd3a7b8d8d8fe13a08","source":{"kind":"arxiv","id":"1611.07541","version":1},"attestation_state":"computed","paper":{"title":"Data Structures for Weighted Matching and Extensions to $b$-matching and $f$-factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Harold N. Gabow","submitted_at":"2016-11-22T21:22:33Z","abstract_excerpt":"This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a data structure for blossom creation. It uses a dynamic nearest-common-ancestor algorithm to simplify blossom steps, so they involve only back edges rather than arbitrary nontree edges.\n  The rest of the paper presents direct extensions of Edmonds' blossom algorithm to weighted $b$-matching and $f$-factors. Again the time bound is the one previously known for b"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.07541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-22T21:22:33Z","cross_cats_sorted":[],"title_canon_sha256":"97791a3984fd307b61766c12c76a31da2c1ed595514813b48fbbd3856d253767","abstract_canon_sha256":"eefeff549ac6d8e395bb3f7a3741f1118f753614da2191c6089e33c04e0dcdc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:00.543250Z","signature_b64":"0ZRgUVLin6lj8/GneNrUVtGV+3mbCr+3SjuMmL8a/5sAIiJt/U21+hQmP3ooNX+l8KLS9HwnFpAw52d+65gTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20b66be67087528fb6770e563e48a3d1b1e90fad853fd8fd3a7b8d8d8fe13a08","last_reissued_at":"2026-05-18T00:57:00.542643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:00.542643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Data Structures for Weighted Matching and Extensions to $b$-matching and $f$-factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Harold N. Gabow","submitted_at":"2016-11-22T21:22:33Z","abstract_excerpt":"This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a data structure for blossom creation. It uses a dynamic nearest-common-ancestor algorithm to simplify blossom steps, so they involve only back edges rather than arbitrary nontree edges.\n  The rest of the paper presents direct extensions of Edmonds' blossom algorithm to weighted $b$-matching and $f$-factors. Again the time bound is the one previously known for b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07541","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.07541","created_at":"2026-05-18T00:57:00.542761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.07541v1","created_at":"2026-05-18T00:57:00.542761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07541","created_at":"2026-05-18T00:57:00.542761+00:00"},{"alias_kind":"pith_short_12","alias_value":"EC3GXZTQQ5JI","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EC3GXZTQQ5JI7NTX","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EC3GXZTQ","created_at":"2026-05-18T12:30:12.583610+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G","json":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G.json","graph_json":"https://pith.science/api/pith-number/EC3GXZTQQ5JI7NTXBZLD4SFD2G/graph.json","events_json":"https://pith.science/api/pith-number/EC3GXZTQQ5JI7NTXBZLD4SFD2G/events.json","paper":"https://pith.science/paper/EC3GXZTQ"},"agent_actions":{"view_html":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G","download_json":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G.json","view_paper":"https://pith.science/paper/EC3GXZTQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.07541&json=true","fetch_graph":"https://pith.science/api/pith-number/EC3GXZTQQ5JI7NTXBZLD4SFD2G/graph.json","fetch_events":"https://pith.science/api/pith-number/EC3GXZTQQ5JI7NTXBZLD4SFD2G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G/action/storage_attestation","attest_author":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G/action/author_attestation","sign_citation":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G/action/citation_signature","submit_replication":"https://pith.science/pith/EC3GXZTQQ5JI7NTXBZLD4SFD2G/action/replication_record"}},"created_at":"2026-05-18T00:57:00.542761+00:00","updated_at":"2026-05-18T00:57:00.542761+00:00"}