{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E3BBVSZXQFXQTM36D3557VDDQH","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":"a93853223947f555e2e41b9624544e45cb6abaaedc7ebd5049b928193c8dbbc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-31T12:30:27Z","title_canon_sha256":"e628437eed8f842905366988e84edfa15b7193c5ff356db4b000e4dd1bbbf80c"},"schema_version":"1.0","source":{"id":"1608.00212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00212","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00212v2","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00212","created_at":"2026-05-18T00:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"E3BBVSZXQFXQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E3BBVSZXQFXQTM36","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E3BBVSZX","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:4862472e9d47a7c04ca55728aaa450ff5efc89a63f742a872efdf02b93c742fa","target":"graph","created_at":"2026-05-18T00:44:33Z","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":"Labeling schemes seek to assign a short label to each node in a network, so that a function on two nodes can be computed by examining their labels alone. For the particular case of trees, optimal bounds (up to low order terms) were recently obtained for adjacency labeling [FOCS'15], nearest common ancestor labeling [SODA'14], and ancestry labeling [SICOMP'06]. In this paper we obtain optimal bounds for distance labeling. We present labels of size $1/4\\log^2n+o(\\log^2n)$, matching (up to low order terms) the recent $1/4\\log^2n-O(\\log n)$ lower bound [ICALP'16].\n  Prior to our work, all distance","authors_text":"Ofer Freedman, Oren Weimann, Patrick K. Nicholson, Pawe{\\l} Gawrychowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-31T12:30:27Z","title":"Optimal Distance Labeling Schemes for Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00212","kind":"arxiv","version":2},"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":"sha256:1ffd4cdeab6f2b3230151a874e98a076953de845f6dffe7a2da14d47827b0f54","target":"record","created_at":"2026-05-18T00:44:33Z","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":"a93853223947f555e2e41b9624544e45cb6abaaedc7ebd5049b928193c8dbbc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-31T12:30:27Z","title_canon_sha256":"e628437eed8f842905366988e84edfa15b7193c5ff356db4b000e4dd1bbbf80c"},"schema_version":"1.0","source":{"id":"1608.00212","kind":"arxiv","version":2}},"canonical_sha256":"26c21acb37816f09b37e1efbdfd46381cd2ed329650bc552d21641eac590653f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26c21acb37816f09b37e1efbdfd46381cd2ed329650bc552d21641eac590653f","first_computed_at":"2026-05-18T00:44:33.755337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:33.755337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lMwNQ2o5NjcxunCE1c6FxGTDQqSc9xeFGP1pMSbGjwmNBu+or5XR3O/G5JCqB+p+DDUfoMKpagkTJc87Y6arCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:33.755790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ffd4cdeab6f2b3230151a874e98a076953de845f6dffe7a2da14d47827b0f54","sha256:4862472e9d47a7c04ca55728aaa450ff5efc89a63f742a872efdf02b93c742fa"],"state_sha256":"5e87b62e6944628158bba7073d1ba5cfc2cb89a0db45ba79e5237dc8fc3f3ef3"}