{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZR3323NUHN453CFXRGP6BO3Q4R","short_pith_number":"pith:ZR3323NU","schema_version":"1.0","canonical_sha256":"cc77bd6db43b79dd88b7899fe0bb70e46f4a10a985ecc2c4795ea60eeb3ea131","source":{"kind":"arxiv","id":"1809.01308","version":1},"attestation_state":"computed","paper":{"title":"Randomized Incremental Construction of Net-Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Donald R. Sheehy, Mahmoodreza Jahanseir","submitted_at":"2018-09-05T03:33:42Z","abstract_excerpt":"Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\\log n)$ time in expectation. Along the way, we define a new, linear-size net-tree variant that simplifies the analyses and algorithms. We show a connection between these trees and approximate Voronoi diagrams and use this to simplify the point location necessary in net-tree construction. Our analysis uses a novel backwards analysis that may be of independent interest."},"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":"1809.01308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-05T03:33:42Z","cross_cats_sorted":[],"title_canon_sha256":"27bf5d4fa6145c9b313a8c9f589de2c720fb271b0c9ec4404c5153757cba437a","abstract_canon_sha256":"c10f6053a77d460400640d6af26aa93d957ab5df20af8bb4ab3db0af0cd6a8e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:28.070374Z","signature_b64":"G/7QFWRDCuRSjM3j3p5UbZf98B7c720wAyqQ9pwgM8lQLFiQ1OreAx7DX5cKCYwjIFJ5b5nwDK+t+8255EXABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc77bd6db43b79dd88b7899fe0bb70e46f4a10a985ecc2c4795ea60eeb3ea131","last_reissued_at":"2026-05-18T00:06:28.069838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:28.069838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Randomized Incremental Construction of Net-Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Donald R. Sheehy, Mahmoodreza Jahanseir","submitted_at":"2018-09-05T03:33:42Z","abstract_excerpt":"Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\\log n)$ time in expectation. Along the way, we define a new, linear-size net-tree variant that simplifies the analyses and algorithms. We show a connection between these trees and approximate Voronoi diagrams and use this to simplify the point location necessary in net-tree construction. Our analysis uses a novel backwards analysis that may be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01308","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":"1809.01308","created_at":"2026-05-18T00:06:28.069916+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01308v1","created_at":"2026-05-18T00:06:28.069916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01308","created_at":"2026-05-18T00:06:28.069916+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZR3323NUHN45","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZR3323NUHN453CFX","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZR3323NU","created_at":"2026-05-18T12:33:07.085635+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/ZR3323NUHN453CFXRGP6BO3Q4R","json":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R.json","graph_json":"https://pith.science/api/pith-number/ZR3323NUHN453CFXRGP6BO3Q4R/graph.json","events_json":"https://pith.science/api/pith-number/ZR3323NUHN453CFXRGP6BO3Q4R/events.json","paper":"https://pith.science/paper/ZR3323NU"},"agent_actions":{"view_html":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R","download_json":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R.json","view_paper":"https://pith.science/paper/ZR3323NU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01308&json=true","fetch_graph":"https://pith.science/api/pith-number/ZR3323NUHN453CFXRGP6BO3Q4R/graph.json","fetch_events":"https://pith.science/api/pith-number/ZR3323NUHN453CFXRGP6BO3Q4R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R/action/storage_attestation","attest_author":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R/action/author_attestation","sign_citation":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R/action/citation_signature","submit_replication":"https://pith.science/pith/ZR3323NUHN453CFXRGP6BO3Q4R/action/replication_record"}},"created_at":"2026-05-18T00:06:28.069916+00:00","updated_at":"2026-05-18T00:06:28.069916+00:00"}