{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IMY4HSF5NQ3WGSKCMCBTEJYNKK","short_pith_number":"pith:IMY4HSF5","schema_version":"1.0","canonical_sha256":"4331c3c8bd6c37634942608332270d52ba0a02860f0f7b8bd4c1b68cdf264616","source":{"kind":"arxiv","id":"1404.0977","version":1},"attestation_state":"computed","paper":{"title":"Faster Shortest Paths in Dense Distance Graphs, with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Oren Weimann, Shay Mozes, Yahav Nussbaum","submitted_at":"2014-04-03T15:44:54Z","abstract_excerpt":"We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol and Rao's algorithm [FOCS'01] for emulating Dijkstra's algorithm on the dense distance graph (DDG). A DDG is defined for a decomposition of a planar graph $G$ into regions of at most $r$ vertices each, for some parameter $r < n$. The vertex set of the DDG is the set of $\\Theta(n/\\sqrt r)$ vertices of $G$ that belong to more than one region (boundary vertice"},"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":"1404.0977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:44:54Z","cross_cats_sorted":[],"title_canon_sha256":"80c78940cbfc84c41505c15c9d67452357d7363d15c4a18cdd80ce76ace69b0f","abstract_canon_sha256":"790d2338d1f18eab2f71c2abe4e8c5d174591039a26588b4dba4d89737f886b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:54.852788Z","signature_b64":"fYZ1dVy6vCPGtotpzoBoXUtV7PW5nVKsdUZDvojo4h9PUwnxiEe7EPkLvx7LCob7q5NFaekrB5BdJnLagOlgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4331c3c8bd6c37634942608332270d52ba0a02860f0f7b8bd4c1b68cdf264616","last_reissued_at":"2026-05-18T02:54:54.852244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:54.852244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faster Shortest Paths in Dense Distance Graphs, with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Oren Weimann, Shay Mozes, Yahav Nussbaum","submitted_at":"2014-04-03T15:44:54Z","abstract_excerpt":"We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol and Rao's algorithm [FOCS'01] for emulating Dijkstra's algorithm on the dense distance graph (DDG). A DDG is defined for a decomposition of a planar graph $G$ into regions of at most $r$ vertices each, for some parameter $r < n$. The vertex set of the DDG is the set of $\\Theta(n/\\sqrt r)$ vertices of $G$ that belong to more than one region (boundary vertice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0977","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":"1404.0977","created_at":"2026-05-18T02:54:54.852350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.0977v1","created_at":"2026-05-18T02:54:54.852350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0977","created_at":"2026-05-18T02:54:54.852350+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMY4HSF5NQ3W","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMY4HSF5NQ3WGSKC","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMY4HSF5","created_at":"2026-05-18T12:28:33.132498+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/IMY4HSF5NQ3WGSKCMCBTEJYNKK","json":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK.json","graph_json":"https://pith.science/api/pith-number/IMY4HSF5NQ3WGSKCMCBTEJYNKK/graph.json","events_json":"https://pith.science/api/pith-number/IMY4HSF5NQ3WGSKCMCBTEJYNKK/events.json","paper":"https://pith.science/paper/IMY4HSF5"},"agent_actions":{"view_html":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK","download_json":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK.json","view_paper":"https://pith.science/paper/IMY4HSF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.0977&json=true","fetch_graph":"https://pith.science/api/pith-number/IMY4HSF5NQ3WGSKCMCBTEJYNKK/graph.json","fetch_events":"https://pith.science/api/pith-number/IMY4HSF5NQ3WGSKCMCBTEJYNKK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK/action/storage_attestation","attest_author":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK/action/author_attestation","sign_citation":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK/action/citation_signature","submit_replication":"https://pith.science/pith/IMY4HSF5NQ3WGSKCMCBTEJYNKK/action/replication_record"}},"created_at":"2026-05-18T02:54:54.852350+00:00","updated_at":"2026-05-18T02:54:54.852350+00:00"}