{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:I37GYVVKGDRE2NXXOA45X6HPBG","short_pith_number":"pith:I37GYVVK","schema_version":"1.0","canonical_sha256":"46fe6c56aa30e24d36f77039dbf8ef099785e53e6bbe1c3aab85aae8120ddd17","source":{"kind":"arxiv","id":"1411.1919","version":6},"attestation_state":"computed","paper":{"title":"Scaling Algorithms for Weighted Matching in General Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hsin-Hao Su, Ran Duan, Seth Pettie","submitted_at":"2014-11-07T14:11:06Z","abstract_excerpt":"We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in $O(m\\sqrt{n}\\log(nN))$ time, $O(m\\sqrt{n})$ per scale, which matches the running time of the best cardinality matching algorithms on sparse graphs. Here $m,n,$ and $N$ bound the number of edges, vertices, and magnitude of any edge weight. Our result improves on a 25-year old algorithm of Gabow and Tarjan, which runs in $O(m\\sqrt{n\\log n\\alpha(m,n)} \\log(nN))$ time."},"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":"1411.1919","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-07T14:11:06Z","cross_cats_sorted":[],"title_canon_sha256":"c5e12b4360c9c488e1f23ee009755c6f6f9eeeaa88db88edfbf9f8f8be6e0cb1","abstract_canon_sha256":"4817cc5f5dbddbf6d1ef001efcacc1ed222d1aecfaef821497208210d6562997"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:32.934610Z","signature_b64":"B64sANdI+Zn8Ni2wavobIEySn8dk3MFMuPkcfFrbDR2Z+Hk15tBkU6d2XDg9hNvknb8zHIm/DlZ2slPOSUHXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46fe6c56aa30e24d36f77039dbf8ef099785e53e6bbe1c3aab85aae8120ddd17","last_reissued_at":"2026-05-18T00:33:32.933988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:32.933988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling Algorithms for Weighted Matching in General Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hsin-Hao Su, Ran Duan, Seth Pettie","submitted_at":"2014-11-07T14:11:06Z","abstract_excerpt":"We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in $O(m\\sqrt{n}\\log(nN))$ time, $O(m\\sqrt{n})$ per scale, which matches the running time of the best cardinality matching algorithms on sparse graphs. Here $m,n,$ and $N$ bound the number of edges, vertices, and magnitude of any edge weight. Our result improves on a 25-year old algorithm of Gabow and Tarjan, which runs in $O(m\\sqrt{n\\log n\\alpha(m,n)} \\log(nN))$ time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1919","kind":"arxiv","version":6},"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":"1411.1919","created_at":"2026-05-18T00:33:32.934096+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1919v6","created_at":"2026-05-18T00:33:32.934096+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1919","created_at":"2026-05-18T00:33:32.934096+00:00"},{"alias_kind":"pith_short_12","alias_value":"I37GYVVKGDRE","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"I37GYVVKGDRE2NXX","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"I37GYVVK","created_at":"2026-05-18T12:28:33.132498+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/I37GYVVKGDRE2NXXOA45X6HPBG","json":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG.json","graph_json":"https://pith.science/api/pith-number/I37GYVVKGDRE2NXXOA45X6HPBG/graph.json","events_json":"https://pith.science/api/pith-number/I37GYVVKGDRE2NXXOA45X6HPBG/events.json","paper":"https://pith.science/paper/I37GYVVK"},"agent_actions":{"view_html":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG","download_json":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG.json","view_paper":"https://pith.science/paper/I37GYVVK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1919&json=true","fetch_graph":"https://pith.science/api/pith-number/I37GYVVKGDRE2NXXOA45X6HPBG/graph.json","fetch_events":"https://pith.science/api/pith-number/I37GYVVKGDRE2NXXOA45X6HPBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG/action/storage_attestation","attest_author":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG/action/author_attestation","sign_citation":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG/action/citation_signature","submit_replication":"https://pith.science/pith/I37GYVVKGDRE2NXXOA45X6HPBG/action/replication_record"}},"created_at":"2026-05-18T00:33:32.934096+00:00","updated_at":"2026-05-18T00:33:32.934096+00:00"}