{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GHJMIA6AS4RGIVDUHDAK2MNBYS","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":"bc17d0ce46672362f5dbbd42a081823c2642745f4cc846f09868bf22c9515ba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-23T21:32:55Z","title_canon_sha256":"d0230c00229ad760eabbf3ad3afa34c78872258465284e9176db62ec0f1ba7f2"},"schema_version":"1.0","source":{"id":"1107.4711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4711","created_at":"2026-05-18T04:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4711v1","created_at":"2026-05-18T04:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4711","created_at":"2026-05-18T04:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"GHJMIA6AS4RG","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GHJMIA6AS4RGIVDU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GHJMIA6A","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:ab296015d74f2b990e2998a819bbafd681efa2bd101c46bcaa0456d881b529e4","target":"graph","created_at":"2026-05-18T04:17:01Z","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 consider the problem of finding all allowed edges in a bipartite graph $G=(V,E)$, i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this computation in linear time $O(n+m)$ (where $n=|V|$ and $m=|E|$). Hence, the time complexity of finding all allowed edges reduces to that of finding a single maximum matching, which is $O(n^{1/2}m)$ [Hopcroft and Karp 1973], or $O((n/\\log n)^{1/2}m)$ for dense graphs with $m=\\Theta(n^2)$ [Alt et al. 1991]. This time complexity improves upon that of the best known algor","authors_text":"Tamir Tassa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-23T21:32:55Z","title":"Finding All Allowed Edges in a Bipartite Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4711","kind":"arxiv","version":1},"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:c526a7e86ca86bb7b380181b672df42120ecad9770a62cf0a2f4f0e4afca018f","target":"record","created_at":"2026-05-18T04:17:01Z","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":"bc17d0ce46672362f5dbbd42a081823c2642745f4cc846f09868bf22c9515ba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-23T21:32:55Z","title_canon_sha256":"d0230c00229ad760eabbf3ad3afa34c78872258465284e9176db62ec0f1ba7f2"},"schema_version":"1.0","source":{"id":"1107.4711","kind":"arxiv","version":1}},"canonical_sha256":"31d2c403c0972264547438c0ad31a1c4808ffa3f52385ba433305e187a7602b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31d2c403c0972264547438c0ad31a1c4808ffa3f52385ba433305e187a7602b4","first_computed_at":"2026-05-18T04:17:01.989498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:01.989498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/wmwwZaEKetFmUeQoXx7PwFy9+GY6jyqW+kXgM9lB7JbeDi0EmaFCRGgTOjWDMiEH5gAZYPEXyFIq/fGIgS7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:01.990109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c526a7e86ca86bb7b380181b672df42120ecad9770a62cf0a2f4f0e4afca018f","sha256:ab296015d74f2b990e2998a819bbafd681efa2bd101c46bcaa0456d881b529e4"],"state_sha256":"a585b660198d11c694e8dfc664be0bbdfabcb8cc57735820cc55b3c6bc56dc87"}