{"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"}