{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GHJMIA6AS4RGIVDUHDAK2MNBYS","short_pith_number":"pith:GHJMIA6A","schema_version":"1.0","canonical_sha256":"31d2c403c0972264547438c0ad31a1c4808ffa3f52385ba433305e187a7602b4","source":{"kind":"arxiv","id":"1107.4711","version":1},"attestation_state":"computed","paper":{"title":"Finding All Allowed Edges in a Bipartite Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Tamir Tassa","submitted_at":"2011-07-23T21:32:55Z","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"},"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":"1107.4711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-23T21:32:55Z","cross_cats_sorted":[],"title_canon_sha256":"d0230c00229ad760eabbf3ad3afa34c78872258465284e9176db62ec0f1ba7f2","abstract_canon_sha256":"bc17d0ce46672362f5dbbd42a081823c2642745f4cc846f09868bf22c9515ba0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:01.990109Z","signature_b64":"/wmwwZaEKetFmUeQoXx7PwFy9+GY6jyqW+kXgM9lB7JbeDi0EmaFCRGgTOjWDMiEH5gAZYPEXyFIq/fGIgS7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31d2c403c0972264547438c0ad31a1c4808ffa3f52385ba433305e187a7602b4","last_reissued_at":"2026-05-18T04:17:01.989498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:01.989498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding All Allowed Edges in a Bipartite Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Tamir Tassa","submitted_at":"2011-07-23T21:32:55Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4711","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":"1107.4711","created_at":"2026-05-18T04:17:01.989607+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4711v1","created_at":"2026-05-18T04:17:01.989607+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4711","created_at":"2026-05-18T04:17:01.989607+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHJMIA6AS4RG","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHJMIA6AS4RGIVDU","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHJMIA6A","created_at":"2026-05-18T12:26:28.662955+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/GHJMIA6AS4RGIVDUHDAK2MNBYS","json":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS.json","graph_json":"https://pith.science/api/pith-number/GHJMIA6AS4RGIVDUHDAK2MNBYS/graph.json","events_json":"https://pith.science/api/pith-number/GHJMIA6AS4RGIVDUHDAK2MNBYS/events.json","paper":"https://pith.science/paper/GHJMIA6A"},"agent_actions":{"view_html":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS","download_json":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS.json","view_paper":"https://pith.science/paper/GHJMIA6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4711&json=true","fetch_graph":"https://pith.science/api/pith-number/GHJMIA6AS4RGIVDUHDAK2MNBYS/graph.json","fetch_events":"https://pith.science/api/pith-number/GHJMIA6AS4RGIVDUHDAK2MNBYS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/action/storage_attestation","attest_author":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/action/author_attestation","sign_citation":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/action/citation_signature","submit_replication":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/action/replication_record"}},"created_at":"2026-05-18T04:17:01.989607+00:00","updated_at":"2026-05-18T04:17:01.989607+00:00"}