{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HFAHX2NETU2BR34WB6E2ZED2Q7","short_pith_number":"pith:HFAHX2NE","schema_version":"1.0","canonical_sha256":"39407be9a49d3418ef960f89ac907a87cf547b0cbabc804845e9f16cf4025d5b","source":{"kind":"arxiv","id":"1412.1001","version":3},"attestation_state":"computed","paper":{"title":"Optimization Algorithms for Faster Computational Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"cs.CG","authors_text":"Yang Yuan, Zeyuan Allen-Zhu, Zhenyu Liao","submitted_at":"2014-12-02T18:15:46Z","abstract_excerpt":"We study two fundamental problems in computational geometry: finding the maximum inscribed ball (MaxIB) inside a bounded polyhedron defined by $m$ hyperplanes, and the minimum enclosing ball (MinEB) of a set of $n$ points, both in $d$-dimensional space. We improve the running time of iterative algorithms on\n  MaxIB from $\\tilde{O}(m d \\alpha^3 / \\varepsilon^3)$ to $\\tilde{O}(md + m \\sqrt{d} \\alpha / \\varepsilon)$, a speed-up up to $\\tilde{O}(\\sqrt{d} \\alpha^2 / \\varepsilon^2)$, and\n  MinEB from $\\tilde{O}(n d / \\sqrt{\\varepsilon})$ to $\\tilde{O}(nd + n \\sqrt{d} / \\sqrt{\\varepsilon})$, a speed-"},"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":"1412.1001","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-12-02T18:15:46Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"9a3cbfd5d5a3deda2df5f17d331f96a2d15017cd2d4c448f851a955ce78d579b","abstract_canon_sha256":"29379c4dffc8929147e337ec137b0ea3c2683d5394a536a7d0da1bd92d599c28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:32.699231Z","signature_b64":"cGTDx5kAs2HTSPotyPQsDGOOoJHYGefKF3o1Lf5bxBKycHk5kf2ZvSD25WOSsmwZ1yhGQmsvzLXbygjzDo9VDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39407be9a49d3418ef960f89ac907a87cf547b0cbabc804845e9f16cf4025d5b","last_reissued_at":"2026-05-18T01:15:32.698488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:32.698488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimization Algorithms for Faster Computational Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"cs.CG","authors_text":"Yang Yuan, Zeyuan Allen-Zhu, Zhenyu Liao","submitted_at":"2014-12-02T18:15:46Z","abstract_excerpt":"We study two fundamental problems in computational geometry: finding the maximum inscribed ball (MaxIB) inside a bounded polyhedron defined by $m$ hyperplanes, and the minimum enclosing ball (MinEB) of a set of $n$ points, both in $d$-dimensional space. We improve the running time of iterative algorithms on\n  MaxIB from $\\tilde{O}(m d \\alpha^3 / \\varepsilon^3)$ to $\\tilde{O}(md + m \\sqrt{d} \\alpha / \\varepsilon)$, a speed-up up to $\\tilde{O}(\\sqrt{d} \\alpha^2 / \\varepsilon^2)$, and\n  MinEB from $\\tilde{O}(n d / \\sqrt{\\varepsilon})$ to $\\tilde{O}(nd + n \\sqrt{d} / \\sqrt{\\varepsilon})$, a speed-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1001","kind":"arxiv","version":3},"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":"1412.1001","created_at":"2026-05-18T01:15:32.698610+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1001v3","created_at":"2026-05-18T01:15:32.698610+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1001","created_at":"2026-05-18T01:15:32.698610+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFAHX2NETU2B","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFAHX2NETU2BR34W","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFAHX2NE","created_at":"2026-05-18T12:28:30.664211+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/HFAHX2NETU2BR34WB6E2ZED2Q7","json":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7.json","graph_json":"https://pith.science/api/pith-number/HFAHX2NETU2BR34WB6E2ZED2Q7/graph.json","events_json":"https://pith.science/api/pith-number/HFAHX2NETU2BR34WB6E2ZED2Q7/events.json","paper":"https://pith.science/paper/HFAHX2NE"},"agent_actions":{"view_html":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7","download_json":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7.json","view_paper":"https://pith.science/paper/HFAHX2NE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1001&json=true","fetch_graph":"https://pith.science/api/pith-number/HFAHX2NETU2BR34WB6E2ZED2Q7/graph.json","fetch_events":"https://pith.science/api/pith-number/HFAHX2NETU2BR34WB6E2ZED2Q7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7/action/storage_attestation","attest_author":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7/action/author_attestation","sign_citation":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7/action/citation_signature","submit_replication":"https://pith.science/pith/HFAHX2NETU2BR34WB6E2ZED2Q7/action/replication_record"}},"created_at":"2026-05-18T01:15:32.698610+00:00","updated_at":"2026-05-18T01:15:32.698610+00:00"}