{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WUVMRZYKUQRLDZPAJHOYNK43UP","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":"a83a3e9f144d1187507897517bb92ae57582603926b536639398c8be0d951d24","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-25T18:39:25Z","title_canon_sha256":"56d66be667c25fb0d10438612d09d17ea812a0166d27d8f89f0035d0b86a9847"},"schema_version":"1.0","source":{"id":"1604.07359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07359","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07359v1","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07359","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"WUVMRZYKUQRL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WUVMRZYKUQRLDZPA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WUVMRZYK","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:72e075149edaeeeaac74917c168af8c508304b201b68a01d32dc4dcbd5eb0815","target":"graph","created_at":"2026-05-18T01:15:57Z","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 provide a quasilinear time algorithm for the $p$-center problem with an additive error less than or equal to 3 times the input graph's hyperbolic constant. Specifically, for the graph $G=(V,E)$ with $n$ vertices, $m$ edges and hyperbolic constant $\\delta$, we construct an algorithm for $p$-centers in time $O(p(\\delta+1)(n+m)\\log(n))$ with radius not exceeding $r_p + \\delta$ when $p \\leq 2$ and $r_p + 3\\delta$ when $p \\geq 3$, where $r_p$ are the optimal radii. Prior work identified $p$-centers with accuracy $r_p+\\delta$ but with time complexity $O((n^3\\log n + n^2m)\\log(diam(G)))$ which is ","authors_text":"Iraj Saniee, Katherine Edwards, W. Sean Kennedy","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-25T18:39:25Z","title":"Fast approximation algorithms for $p$-centres in large $\\delta$-hyperbolic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07359","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":"sha256:4ebfedb5107d4831492518a74ae9557520063bd1a04c64e61a94f89307e180c3","target":"record","created_at":"2026-05-18T01:15:57Z","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":"a83a3e9f144d1187507897517bb92ae57582603926b536639398c8be0d951d24","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-25T18:39:25Z","title_canon_sha256":"56d66be667c25fb0d10438612d09d17ea812a0166d27d8f89f0035d0b86a9847"},"schema_version":"1.0","source":{"id":"1604.07359","kind":"arxiv","version":1}},"canonical_sha256":"b52ac8e70aa422b1e5e049dd86ab9ba3d01179b24f7e120693c3bc24fefa4271","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b52ac8e70aa422b1e5e049dd86ab9ba3d01179b24f7e120693c3bc24fefa4271","first_computed_at":"2026-05-18T01:15:57.197462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:57.197462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0+7HbUmCnDzA3qlwSgyy055Yidl6lFbupHtjRYvmRy/wJ9P+P3IgTvIgdzrlqe8CVScObv/0oK3GI8JNRqfdAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:57.197985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.07359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ebfedb5107d4831492518a74ae9557520063bd1a04c64e61a94f89307e180c3","sha256:72e075149edaeeeaac74917c168af8c508304b201b68a01d32dc4dcbd5eb0815"],"state_sha256":"7f587c192757c226006a8649f5ca487ac028694dafc11ab37bed140e189d0de2"}