{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:55P7O6WNALVB2AKMGJZGNZDWCR","short_pith_number":"pith:55P7O6WN","schema_version":"1.0","canonical_sha256":"ef5ff77acd02ea1d014c327266e4761440b63a6c904bff0b69ac6513c5f4415d","source":{"kind":"arxiv","id":"1702.07815","version":2},"attestation_state":"computed","paper":{"title":"Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Sergio Cabello","submitted_at":"2017-02-25T01:24:03Z","abstract_excerpt":"We show how to compute for $n$-vertex planar graphs in $O(n^{11/6}{\\rm polylog}(n))$ expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In $O(n^{15/8}{\\rm polylog}(n))$ expected time we can also compute the number of pairs of vertices at distance smaller than a given threshold. These are the first algorithms for these problems using time $O(n^c)$ for some constant $c<2$, even when restricted to undirected, unweighted planar graphs."},"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":"1702.07815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-25T01:24:03Z","cross_cats_sorted":[],"title_canon_sha256":"6d8e845af9941767cb6a7d034a265f05f4e624b3d76921fa1c1fdaad8c164fbf","abstract_canon_sha256":"87423592e7b9338b7b67e472cd2fc9311d57390ec76ecc93f8394ecdcce1d437"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:14.696689Z","signature_b64":"cH0LGLon/tR4Hyh+4b/401jxDlPI67X4RQ6D9IS8Lo0IRMj6G6regpnJCtB6+ME8WxBeL9zbcH+h5QnL/3+oAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef5ff77acd02ea1d014c327266e4761440b63a6c904bff0b69ac6513c5f4415d","last_reissued_at":"2026-05-18T00:16:14.695918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:14.695918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Sergio Cabello","submitted_at":"2017-02-25T01:24:03Z","abstract_excerpt":"We show how to compute for $n$-vertex planar graphs in $O(n^{11/6}{\\rm polylog}(n))$ expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In $O(n^{15/8}{\\rm polylog}(n))$ expected time we can also compute the number of pairs of vertices at distance smaller than a given threshold. These are the first algorithms for these problems using time $O(n^c)$ for some constant $c<2$, even when restricted to undirected, unweighted planar graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07815","kind":"arxiv","version":2},"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":"1702.07815","created_at":"2026-05-18T00:16:14.696065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.07815v2","created_at":"2026-05-18T00:16:14.696065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07815","created_at":"2026-05-18T00:16:14.696065+00:00"},{"alias_kind":"pith_short_12","alias_value":"55P7O6WNALVB","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"55P7O6WNALVB2AKM","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"55P7O6WN","created_at":"2026-05-18T12:31:00.734936+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/55P7O6WNALVB2AKMGJZGNZDWCR","json":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR.json","graph_json":"https://pith.science/api/pith-number/55P7O6WNALVB2AKMGJZGNZDWCR/graph.json","events_json":"https://pith.science/api/pith-number/55P7O6WNALVB2AKMGJZGNZDWCR/events.json","paper":"https://pith.science/paper/55P7O6WN"},"agent_actions":{"view_html":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR","download_json":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR.json","view_paper":"https://pith.science/paper/55P7O6WN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.07815&json=true","fetch_graph":"https://pith.science/api/pith-number/55P7O6WNALVB2AKMGJZGNZDWCR/graph.json","fetch_events":"https://pith.science/api/pith-number/55P7O6WNALVB2AKMGJZGNZDWCR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR/action/storage_attestation","attest_author":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR/action/author_attestation","sign_citation":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR/action/citation_signature","submit_replication":"https://pith.science/pith/55P7O6WNALVB2AKMGJZGNZDWCR/action/replication_record"}},"created_at":"2026-05-18T00:16:14.696065+00:00","updated_at":"2026-05-18T00:16:14.696065+00:00"}