{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I37GYVVKGDRE2NXXOA45X6HPBG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4817cc5f5dbddbf6d1ef001efcacc1ed222d1aecfaef821497208210d6562997","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-07T14:11:06Z","title_canon_sha256":"c5e12b4360c9c488e1f23ee009755c6f6f9eeeaa88db88edfbf9f8f8be6e0cb1"},"schema_version":"1.0","source":{"id":"1411.1919","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1919","created_at":"2026-05-18T00:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1919v6","created_at":"2026-05-18T00:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1919","created_at":"2026-05-18T00:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"I37GYVVKGDRE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I37GYVVKGDRE2NXX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I37GYVVK","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:d7f83043431bd860aad6ab3a69d0fe19e036e8d622a0f94cecb66f0975b3c0c6","target":"graph","created_at":"2026-05-18T00:33:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Hsin-Hao Su, Ran Duan, Seth Pettie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-07T14:11:06Z","title":"Scaling Algorithms for Weighted Matching in General Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1919","kind":"arxiv","version":6},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cbebd3d4878b08f6af3d571f2e6ae764e153ba63449ff847180baa6a9bab4c87","target":"record","created_at":"2026-05-18T00:33:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4817cc5f5dbddbf6d1ef001efcacc1ed222d1aecfaef821497208210d6562997","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-07T14:11:06Z","title_canon_sha256":"c5e12b4360c9c488e1f23ee009755c6f6f9eeeaa88db88edfbf9f8f8be6e0cb1"},"schema_version":"1.0","source":{"id":"1411.1919","kind":"arxiv","version":6}},"canonical_sha256":"46fe6c56aa30e24d36f77039dbf8ef099785e53e6bbe1c3aab85aae8120ddd17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46fe6c56aa30e24d36f77039dbf8ef099785e53e6bbe1c3aab85aae8120ddd17","first_computed_at":"2026-05-18T00:33:32.933988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:32.933988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B64sANdI+Zn8Ni2wavobIEySn8dk3MFMuPkcfFrbDR2Z+Hk15tBkU6d2XDg9hNvknb8zHIm/DlZ2slPOSUHXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:32.934610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1919","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbebd3d4878b08f6af3d571f2e6ae764e153ba63449ff847180baa6a9bab4c87","sha256:d7f83043431bd860aad6ab3a69d0fe19e036e8d622a0f94cecb66f0975b3c0c6"],"state_sha256":"4bbd4eccd1aefbaa449a26b69488d8aebf69ba49febae2313f0858cc53bbbfe1"}