{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GHJMIA6AS4RGIVDUHDAK2MNBYS","short_pith_number":"pith:GHJMIA6A","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"},"canonical_sha256":"31d2c403c0972264547438c0ad31a1c4808ffa3f52385ba433305e187a7602b4","source":{"kind":"arxiv","id":"1107.4711","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GHJMIA6AS4RGIVDUHDAK2MNBYS","target":"record","payload":{"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"},"canonical_sha256":"31d2c403c0972264547438c0ad31a1c4808ffa3f52385ba433305e187a7602b4","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"},"source_kind":"arxiv","source_id":"1107.4711","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvFMyAJnJHschYCONDTyJMsoI27FEq234zqhKT1vWDNIlGinI+4KAPzrPF7jZvUGtTiP4QrOzADM7dJHqIxbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:44:36.424613Z"},"content_sha256":"c526a7e86ca86bb7b380181b672df42120ecad9770a62cf0a2f4f0e4afca018f","schema_version":"1.0","event_id":"sha256:c526a7e86ca86bb7b380181b672df42120ecad9770a62cf0a2f4f0e4afca018f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GHJMIA6AS4RGIVDUHDAK2MNBYS","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/s7PY5LQhIIQPC/3zUCMeGT+UoXaiVG4NXtG7k/q2ztptsW8kl0/BpKv515HAxKkWpwwJu4AOR/a/gf7d+mTCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:44:36.424953Z"},"content_sha256":"ab296015d74f2b990e2998a819bbafd681efa2bd101c46bcaa0456d881b529e4","schema_version":"1.0","event_id":"sha256:ab296015d74f2b990e2998a819bbafd681efa2bd101c46bcaa0456d881b529e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/bundle.json","state_url":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T07:44:36Z","links":{"resolver":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS","bundle":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/bundle.json","state":"https://pith.science/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHJMIA6AS4RGIVDUHDAK2MNBYS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kQB1tIreGNux0aDG6qHcxZ7/iBTxkz6FLaIYbthmGbXz0JR1LHXBSz7P1887OjpJbAoCpPch1JCkd6Vywh9TBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:44:36.426789Z","bundle_sha256":"7fa81f4e32e6e48eae9c83615dada0d7c95abb6fa222b3af43aedecc29821d28"}}