{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:QUK2JM5MCVOECY65YBZIQ57BXS","short_pith_number":"pith:QUK2JM5M","schema_version":"1.0","canonical_sha256":"8515a4b3ac155c4163ddc0728877e1bc8ed5a590e2d351550523645115d0c5d3","source":{"kind":"arxiv","id":"2011.09591","version":1},"attestation_state":"computed","paper":{"title":"Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Haitao Wang, Yiming Zhao","submitted_at":"2020-11-19T00:07:43Z","abstract_excerpt":"We consider the problem of computing the diameter of a unicycle graph (i.e., a graph with a unique cycle). We present an O(n) time algorithm for the problem, where n is the number of vertices of the graph. This improves the previous best O(n \\log n) time solution [Oh and Ahn, ISAAC 2016]. Using this algorithm as a subroutine, we solve the problem of adding a shortcut to a tree so that the diameter of the new graph (which is a unicycle graph) is minimized; our algorithm takes O(n^2 \\log n) time and O(n) space. The previous best algorithms solve the problem in O(n^2 \\log^3 n) time and O(n) space"},"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":"2011.09591","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-11-19T00:07:43Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"0d59a4f6e703dcc2e443275ec00b64061738dd0209c4120461d72088aaf05be6","abstract_canon_sha256":"d6ff03b1565b5b4076426e561020c48f1c7b822e507f0f1f78d28b6de6ae2046"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:50.203884Z","signature_b64":"KnpQbomf0J1PGKwvwYCE4rAU0F7K13w8B8WU5Gn4CJ27C21m3rSaOaOaV644M1ZUabWtEJlydrUFXwlfJiBaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8515a4b3ac155c4163ddc0728877e1bc8ed5a590e2d351550523645115d0c5d3","last_reissued_at":"2026-07-05T01:52:50.203465Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:50.203465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Haitao Wang, Yiming Zhao","submitted_at":"2020-11-19T00:07:43Z","abstract_excerpt":"We consider the problem of computing the diameter of a unicycle graph (i.e., a graph with a unique cycle). We present an O(n) time algorithm for the problem, where n is the number of vertices of the graph. This improves the previous best O(n \\log n) time solution [Oh and Ahn, ISAAC 2016]. Using this algorithm as a subroutine, we solve the problem of adding a shortcut to a tree so that the diameter of the new graph (which is a unicycle graph) is minimized; our algorithm takes O(n^2 \\log n) time and O(n) space. The previous best algorithms solve the problem in O(n^2 \\log^3 n) time and O(n) space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09591","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.09591/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2011.09591","created_at":"2026-07-05T01:52:50.203521+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.09591v1","created_at":"2026-07-05T01:52:50.203521+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09591","created_at":"2026-07-05T01:52:50.203521+00:00"},{"alias_kind":"pith_short_12","alias_value":"QUK2JM5MCVOE","created_at":"2026-07-05T01:52:50.203521+00:00"},{"alias_kind":"pith_short_16","alias_value":"QUK2JM5MCVOECY65","created_at":"2026-07-05T01:52:50.203521+00:00"},{"alias_kind":"pith_short_8","alias_value":"QUK2JM5M","created_at":"2026-07-05T01:52:50.203521+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/QUK2JM5MCVOECY65YBZIQ57BXS","json":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS.json","graph_json":"https://pith.science/api/pith-number/QUK2JM5MCVOECY65YBZIQ57BXS/graph.json","events_json":"https://pith.science/api/pith-number/QUK2JM5MCVOECY65YBZIQ57BXS/events.json","paper":"https://pith.science/paper/QUK2JM5M"},"agent_actions":{"view_html":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS","download_json":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS.json","view_paper":"https://pith.science/paper/QUK2JM5M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.09591&json=true","fetch_graph":"https://pith.science/api/pith-number/QUK2JM5MCVOECY65YBZIQ57BXS/graph.json","fetch_events":"https://pith.science/api/pith-number/QUK2JM5MCVOECY65YBZIQ57BXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/action/storage_attestation","attest_author":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/action/author_attestation","sign_citation":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/action/citation_signature","submit_replication":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/action/replication_record"}},"created_at":"2026-07-05T01:52:50.203521+00:00","updated_at":"2026-07-05T01:52:50.203521+00:00"}