{"paper":{"title":"Closest-Pair Queries in Fat Rectangles","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Michiel Smid, Sang Won Bae","submitted_at":"2018-09-27T14:15:33Z","abstract_excerpt":"In the range closest pair problem, we want to construct a data structure storing a set $S$ of $n$ points in the plane, such that for any axes-parallel query rectangle $R$, the closest pair in the set $R \\cap S$ can be reported. The currently best result for this problem is by Xue et al.~(SoCG 2018). Their data structure has size $O(n \\log^2 n)$ and query time $O(\\log^2 n)$. We show that a data structure of size $O(n \\log n)$ can be constructed in $O(n \\log n)$ time, such that queries can be answered in $O(\\log n + f \\log f)$ time, where $f$ is the aspect ratio of $R$. Thus, for fat query recta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10531","kind":"arxiv","version":2},"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"}