{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LNJEB4MQPS3BXFY35I7I3WSAWS","short_pith_number":"pith:LNJEB4MQ","schema_version":"1.0","canonical_sha256":"5b5240f1907cb61b971bea3e8dda40b48ce4ec05fe3ab20ef8b380e4da216c52","source":{"kind":"arxiv","id":"1607.04755","version":2},"attestation_state":"computed","paper":{"title":"High-dimensional approximate $r$-nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Georgia Avarikioti, Ioannis Psarros, Ioannis Z. Emiris, Loukas Kavouras","submitted_at":"2016-07-16T15:53:07Z","abstract_excerpt":"The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean distance. For any fixed $\\epsilon>0$, the approximation factor is $1+\\epsilon$ and the complexity is polynomial in the dimension and subquadratic in the number of points. The algorithm succeeds with high probability. More specifically, the best previously known LSH-based construction of Eppstein et al.\\ \\cite{EHS15} is improved in terms of complexity by reduc"},"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":"1607.04755","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-07-16T15:53:07Z","cross_cats_sorted":[],"title_canon_sha256":"e2eafa48aecce5a46fa7936b0aa7946f9050eff48aa88ff9bc5e4c01f934c456","abstract_canon_sha256":"b380ab15a9f03657648f689f0efd1210addd63e8dfa3b0d1bacc2fff7be96414"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:57.894016Z","signature_b64":"do8hAh2dTSx9zXbwkjWJAmrfZ2LYNK/haI40RSPH//49BEtvi46tMhN2PK1bckY33QkygnMoKYrOCm95R48hCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b5240f1907cb61b971bea3e8dda40b48ce4ec05fe3ab20ef8b380e4da216c52","last_reissued_at":"2026-05-18T00:44:57.893429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:57.893429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High-dimensional approximate $r$-nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Georgia Avarikioti, Ioannis Psarros, Ioannis Z. Emiris, Loukas Kavouras","submitted_at":"2016-07-16T15:53:07Z","abstract_excerpt":"The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean distance. For any fixed $\\epsilon>0$, the approximation factor is $1+\\epsilon$ and the complexity is polynomial in the dimension and subquadratic in the number of points. The algorithm succeeds with high probability. More specifically, the best previously known LSH-based construction of Eppstein et al.\\ \\cite{EHS15} is improved in terms of complexity by reduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04755","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":"1607.04755","created_at":"2026-05-18T00:44:57.893516+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.04755v2","created_at":"2026-05-18T00:44:57.893516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04755","created_at":"2026-05-18T00:44:57.893516+00:00"},{"alias_kind":"pith_short_12","alias_value":"LNJEB4MQPS3B","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LNJEB4MQPS3BXFY3","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LNJEB4MQ","created_at":"2026-05-18T12:30:29.479603+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/LNJEB4MQPS3BXFY35I7I3WSAWS","json":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS.json","graph_json":"https://pith.science/api/pith-number/LNJEB4MQPS3BXFY35I7I3WSAWS/graph.json","events_json":"https://pith.science/api/pith-number/LNJEB4MQPS3BXFY35I7I3WSAWS/events.json","paper":"https://pith.science/paper/LNJEB4MQ"},"agent_actions":{"view_html":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS","download_json":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS.json","view_paper":"https://pith.science/paper/LNJEB4MQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.04755&json=true","fetch_graph":"https://pith.science/api/pith-number/LNJEB4MQPS3BXFY35I7I3WSAWS/graph.json","fetch_events":"https://pith.science/api/pith-number/LNJEB4MQPS3BXFY35I7I3WSAWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS/action/storage_attestation","attest_author":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS/action/author_attestation","sign_citation":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS/action/citation_signature","submit_replication":"https://pith.science/pith/LNJEB4MQPS3BXFY35I7I3WSAWS/action/replication_record"}},"created_at":"2026-05-18T00:44:57.893516+00:00","updated_at":"2026-05-18T00:44:57.893516+00:00"}