{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TN2FCZKXK4IBP4ACL3ESDNZWJI","short_pith_number":"pith:TN2FCZKX","schema_version":"1.0","canonical_sha256":"9b74516557571017f0025ec921b7364a0fa9db12f8f441d970b11d914718c044","source":{"kind":"arxiv","id":"1609.08723","version":1},"attestation_state":"computed","paper":{"title":"Cut Tree Construction from Massive Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.DS","authors_text":"Naoto Mizuno, Takuya Akiba, Yoichi Iwata, Yosuke Sameshima, Yosuke Yano","submitted_at":"2016-09-28T01:49:46Z","abstract_excerpt":"The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining, as they support various procedures related to the minimum cut, maximum flow, and connectivity. However, the crucial drawback with cut trees is the computational cost of their construction. In theory, a cut tree is built by applying a maximum flow algorithm for $n$ times, where $n$ is the number of vertices. Therefore, naive implementations of this approach re"},"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":"1609.08723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T01:49:46Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"97b4583aef747376c653ea8b156deae80e4941fe0c90de6f7597756f504ffd52","abstract_canon_sha256":"fd67ba2069b3572c4a3468da19f24a7be40a7bde886f92568c83127169208621"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:42.095718Z","signature_b64":"YqRy7+MV1bJtX0I2OeaKeJoCH5eH6KqnHC+XX4DDVRWgspHXpzF/O1m8VOjOfRUZ/rL4HgmF2U1QPHUH+apVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b74516557571017f0025ec921b7364a0fa9db12f8f441d970b11d914718c044","last_reissued_at":"2026-05-18T01:03:42.095261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:42.095261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cut Tree Construction from Massive Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.DS","authors_text":"Naoto Mizuno, Takuya Akiba, Yoichi Iwata, Yosuke Sameshima, Yosuke Yano","submitted_at":"2016-09-28T01:49:46Z","abstract_excerpt":"The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining, as they support various procedures related to the minimum cut, maximum flow, and connectivity. However, the crucial drawback with cut trees is the computational cost of their construction. In theory, a cut tree is built by applying a maximum flow algorithm for $n$ times, where $n$ is the number of vertices. Therefore, naive implementations of this approach re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08723","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":"1609.08723","created_at":"2026-05-18T01:03:42.095326+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.08723v1","created_at":"2026-05-18T01:03:42.095326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08723","created_at":"2026-05-18T01:03:42.095326+00:00"},{"alias_kind":"pith_short_12","alias_value":"TN2FCZKXK4IB","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TN2FCZKXK4IBP4AC","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TN2FCZKX","created_at":"2026-05-18T12:30:44.179134+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/TN2FCZKXK4IBP4ACL3ESDNZWJI","json":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI.json","graph_json":"https://pith.science/api/pith-number/TN2FCZKXK4IBP4ACL3ESDNZWJI/graph.json","events_json":"https://pith.science/api/pith-number/TN2FCZKXK4IBP4ACL3ESDNZWJI/events.json","paper":"https://pith.science/paper/TN2FCZKX"},"agent_actions":{"view_html":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI","download_json":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI.json","view_paper":"https://pith.science/paper/TN2FCZKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.08723&json=true","fetch_graph":"https://pith.science/api/pith-number/TN2FCZKXK4IBP4ACL3ESDNZWJI/graph.json","fetch_events":"https://pith.science/api/pith-number/TN2FCZKXK4IBP4ACL3ESDNZWJI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/action/storage_attestation","attest_author":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/action/author_attestation","sign_citation":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/action/citation_signature","submit_replication":"https://pith.science/pith/TN2FCZKXK4IBP4ACL3ESDNZWJI/action/replication_record"}},"created_at":"2026-05-18T01:03:42.095326+00:00","updated_at":"2026-05-18T01:03:42.095326+00:00"}