{"paper":{"title":"Finding Pairwise Intersections of Rectangles in a Query Rectangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Eunjin Oh, Hee-Kap Ahn","submitted_at":"2018-01-23T00:55:35Z","abstract_excerpt":"We consider the following problem: Preprocess a set $\\mathcal{S}$ of $n$ axis-parallel boxes in $\\mathbb{R}^d$ so that given a query of an axis-parallel box in $\\mathbb{R}^d$, the pairs of boxes of $\\mathcal{S}$ whose intersection intersects the query box can be reported efficiently. For the case that $d=2$, we present a data structure of size $O(n\\log n)$ supporting $O(\\log n+k)$ query time, where $k$ is the size of the output. This improves the previously best known result by de Berg et al. which requires $O(\\log n+ k\\log n)$ query time using $O(n\\log n)$ space. There has been no result know"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07362","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"}