{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ZX5HZYOOU2U57LVCGU24Q3U5J6","short_pith_number":"pith:ZX5HZYOO","schema_version":"1.0","canonical_sha256":"cdfa7ce1cea6a9dfaea23535c86e9d4f92f0a9703838373493c825bcf3f6e6af","source":{"kind":"arxiv","id":"1903.08387","version":1},"attestation_state":"computed","paper":{"title":"Dynamic Geometric Data Structures via Shallow Cuttings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Timothy M. Chan","submitted_at":"2019-03-20T08:35:19Z","abstract_excerpt":"We present new results on a number of fundamental problems about dynamic geometric data structures:\n  1. We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or the volume of the convex hull of a 3D point set, (ii) the largest empty circle for a 2D point set, (iii) the Hausdorff distance between two 2D point sets, (iv) the discrete 1-center of a 2D point set, (v)the number of maximal (i.e., skyline) points in a 3D point set. The update times are near $n^{11/12}$ for (i) and (ii), $n^{7/8}$ for (iii) and (iv), and $n"},"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":"1903.08387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-03-20T08:35:19Z","cross_cats_sorted":[],"title_canon_sha256":"4650bbd7d638ed71718ef3543d8ea9c3305c3a18256d636becbf1a49626fa8af","abstract_canon_sha256":"b1bc9a379ff049a2a356e663704ba7dfb2f87adbbca3b4268335c51013aec78f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:48.241955Z","signature_b64":"SuwyOk7CZLVSAkbh6pq0CqSgzFqDS9XB+T8PJYzEX7iRFP24zzsN3cWZkaM0dY/IRwbQNrPhtMcRrvAY632CCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdfa7ce1cea6a9dfaea23535c86e9d4f92f0a9703838373493c825bcf3f6e6af","last_reissued_at":"2026-05-17T23:50:48.241199Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:48.241199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamic Geometric Data Structures via Shallow Cuttings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Timothy M. Chan","submitted_at":"2019-03-20T08:35:19Z","abstract_excerpt":"We present new results on a number of fundamental problems about dynamic geometric data structures:\n  1. We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or the volume of the convex hull of a 3D point set, (ii) the largest empty circle for a 2D point set, (iii) the Hausdorff distance between two 2D point sets, (iv) the discrete 1-center of a 2D point set, (v)the number of maximal (i.e., skyline) points in a 3D point set. The update times are near $n^{11/12}$ for (i) and (ii), $n^{7/8}$ for (iii) and (iv), and $n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08387","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":"1903.08387","created_at":"2026-05-17T23:50:48.241335+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.08387v1","created_at":"2026-05-17T23:50:48.241335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08387","created_at":"2026-05-17T23:50:48.241335+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZX5HZYOOU2U5","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZX5HZYOOU2U57LVC","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZX5HZYOO","created_at":"2026-05-18T12:33:33.725879+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/ZX5HZYOOU2U57LVCGU24Q3U5J6","json":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6.json","graph_json":"https://pith.science/api/pith-number/ZX5HZYOOU2U57LVCGU24Q3U5J6/graph.json","events_json":"https://pith.science/api/pith-number/ZX5HZYOOU2U57LVCGU24Q3U5J6/events.json","paper":"https://pith.science/paper/ZX5HZYOO"},"agent_actions":{"view_html":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6","download_json":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6.json","view_paper":"https://pith.science/paper/ZX5HZYOO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.08387&json=true","fetch_graph":"https://pith.science/api/pith-number/ZX5HZYOOU2U57LVCGU24Q3U5J6/graph.json","fetch_events":"https://pith.science/api/pith-number/ZX5HZYOOU2U57LVCGU24Q3U5J6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6/action/storage_attestation","attest_author":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6/action/author_attestation","sign_citation":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6/action/citation_signature","submit_replication":"https://pith.science/pith/ZX5HZYOOU2U57LVCGU24Q3U5J6/action/replication_record"}},"created_at":"2026-05-17T23:50:48.241335+00:00","updated_at":"2026-05-17T23:50:48.241335+00:00"}