{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:QM6SAD4WKGORJLAUV4W6V7TI4L","short_pith_number":"pith:QM6SAD4W","schema_version":"1.0","canonical_sha256":"833d200f96519d14ac14af2deafe68e2efd11fd4f74d9d1580a675a67b927619","source":{"kind":"arxiv","id":"1901.01763","version":1},"attestation_state":"computed","paper":{"title":"Approximate Discontinuous Trajectory Hotspots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ali Gholami Rudi","submitted_at":"2019-01-07T12:01:26Z","abstract_excerpt":"A hotspot is an axis-aligned square of fixed side length $s$, the duration of the presence of an entity moving in the plane in which is maximised. An exact hotspot of a polygonal trajectory with $n$ edges can be found in $O(n^2)$. Defining a $c$-approximate hotspot as an axis-aligned square of side length $cs$, in which the duration of the entity's presence is no less than that of an exact hotspot, in this paper we present an algorithm to find a $(1 + \\epsilon)$-approximate hotspot of a polygonal trajectory with the time complexity $O({n\\phi \\over \\epsilon} \\log {n\\phi \\over \\epsilon})$, where"},"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":"1901.01763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-01-07T12:01:26Z","cross_cats_sorted":[],"title_canon_sha256":"fdf1ed2bd2df440841cf65c30b553dac479169e5484a685463ddf310d6e91c9d","abstract_canon_sha256":"5532fdba34a449df69f6b96ba4cdc1c9209d074df7ba1f130c4ac625d8e15f36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:51.291195Z","signature_b64":"e4I7NTDHacK7ANKCQ6+/MySQXHVaNUai5sLE2JtCvBWRBG72CZltgD3F95QXnQOgHHmZ4kLuWvaHiFQRjkXuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"833d200f96519d14ac14af2deafe68e2efd11fd4f74d9d1580a675a67b927619","last_reissued_at":"2026-05-17T23:56:51.290656Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:51.290656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate Discontinuous Trajectory Hotspots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ali Gholami Rudi","submitted_at":"2019-01-07T12:01:26Z","abstract_excerpt":"A hotspot is an axis-aligned square of fixed side length $s$, the duration of the presence of an entity moving in the plane in which is maximised. An exact hotspot of a polygonal trajectory with $n$ edges can be found in $O(n^2)$. Defining a $c$-approximate hotspot as an axis-aligned square of side length $cs$, in which the duration of the entity's presence is no less than that of an exact hotspot, in this paper we present an algorithm to find a $(1 + \\epsilon)$-approximate hotspot of a polygonal trajectory with the time complexity $O({n\\phi \\over \\epsilon} \\log {n\\phi \\over \\epsilon})$, where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01763","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":"1901.01763","created_at":"2026-05-17T23:56:51.290744+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01763v1","created_at":"2026-05-17T23:56:51.290744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01763","created_at":"2026-05-17T23:56:51.290744+00:00"},{"alias_kind":"pith_short_12","alias_value":"QM6SAD4WKGOR","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"QM6SAD4WKGORJLAU","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"QM6SAD4W","created_at":"2026-05-18T12:33:27.125529+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/QM6SAD4WKGORJLAUV4W6V7TI4L","json":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L.json","graph_json":"https://pith.science/api/pith-number/QM6SAD4WKGORJLAUV4W6V7TI4L/graph.json","events_json":"https://pith.science/api/pith-number/QM6SAD4WKGORJLAUV4W6V7TI4L/events.json","paper":"https://pith.science/paper/QM6SAD4W"},"agent_actions":{"view_html":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L","download_json":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L.json","view_paper":"https://pith.science/paper/QM6SAD4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01763&json=true","fetch_graph":"https://pith.science/api/pith-number/QM6SAD4WKGORJLAUV4W6V7TI4L/graph.json","fetch_events":"https://pith.science/api/pith-number/QM6SAD4WKGORJLAUV4W6V7TI4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L/action/storage_attestation","attest_author":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L/action/author_attestation","sign_citation":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L/action/citation_signature","submit_replication":"https://pith.science/pith/QM6SAD4WKGORJLAUV4W6V7TI4L/action/replication_record"}},"created_at":"2026-05-17T23:56:51.290744+00:00","updated_at":"2026-05-17T23:56:51.290744+00:00"}