{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7ISH366CXN7IHCCKZY4WIPDYFG","short_pith_number":"pith:7ISH366C","schema_version":"1.0","canonical_sha256":"fa247dfbc2bb7e83884ace39643c7829ab875a0fc4a088088f77ddb9cb88f01c","source":{"kind":"arxiv","id":"1610.08543","version":7},"attestation_state":"computed","paper":{"title":"An efficient approximation for point-set diameter in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ali Mohades, Mahdi Imanparast, Seyed Naser Hashemi","submitted_at":"2016-10-26T20:40:09Z","abstract_excerpt":"In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\\varepsilon)$-approximation algorithm with $O(n+ 1/\\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \\varepsilon\\leqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(\\varepsilon))$-approximation algorithm with $O(n+ 1/\\varepsilon^{\\frac{2d}{3}-\\frac{1}{3}})$ running time. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure."},"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":"1610.08543","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-10-26T20:40:09Z","cross_cats_sorted":[],"title_canon_sha256":"f132cab35b52258886cbbd44ca4e9ee2b192457aa05d2022333c2f3f57254f02","abstract_canon_sha256":"e6be62908232c4666663257711d22ab0edf921b82f6482cb5067eec423c00ce9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:55.810655Z","signature_b64":"lcX+Ume+R/oSk+xlM/r37ClTRwAukwgLzqY2X225pqTZnQfi0WPBT67X/Woqm4jQleiKDY2RIPQE74CbKti5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa247dfbc2bb7e83884ace39643c7829ab875a0fc4a088088f77ddb9cb88f01c","last_reissued_at":"2026-05-17T23:46:55.810202Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:55.810202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An efficient approximation for point-set diameter in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ali Mohades, Mahdi Imanparast, Seyed Naser Hashemi","submitted_at":"2016-10-26T20:40:09Z","abstract_excerpt":"In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\\varepsilon)$-approximation algorithm with $O(n+ 1/\\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \\varepsilon\\leqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(\\varepsilon))$-approximation algorithm with $O(n+ 1/\\varepsilon^{\\frac{2d}{3}-\\frac{1}{3}})$ running time. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08543","kind":"arxiv","version":7},"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":"1610.08543","created_at":"2026-05-17T23:46:55.810265+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.08543v7","created_at":"2026-05-17T23:46:55.810265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08543","created_at":"2026-05-17T23:46:55.810265+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ISH366CXN7I","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ISH366CXN7IHCCK","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ISH366C","created_at":"2026-05-18T12:30:04.600751+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/7ISH366CXN7IHCCKZY4WIPDYFG","json":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG.json","graph_json":"https://pith.science/api/pith-number/7ISH366CXN7IHCCKZY4WIPDYFG/graph.json","events_json":"https://pith.science/api/pith-number/7ISH366CXN7IHCCKZY4WIPDYFG/events.json","paper":"https://pith.science/paper/7ISH366C"},"agent_actions":{"view_html":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG","download_json":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG.json","view_paper":"https://pith.science/paper/7ISH366C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.08543&json=true","fetch_graph":"https://pith.science/api/pith-number/7ISH366CXN7IHCCKZY4WIPDYFG/graph.json","fetch_events":"https://pith.science/api/pith-number/7ISH366CXN7IHCCKZY4WIPDYFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/action/storage_attestation","attest_author":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/action/author_attestation","sign_citation":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/action/citation_signature","submit_replication":"https://pith.science/pith/7ISH366CXN7IHCCKZY4WIPDYFG/action/replication_record"}},"created_at":"2026-05-17T23:46:55.810265+00:00","updated_at":"2026-05-17T23:46:55.810265+00:00"}