{"paper":{"title":"Distance-Sensitive Planar Point Location","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Bettina Speckmann, Boris Aronov, David Eppstein, Marcel Roeloffzen, Mark de Berg","submitted_at":"2016-02-02T02:23:55Z","abstract_excerpt":"Let $\\mathcal{S}$ be a connected planar polygonal subdivision with $n$ edges that we want to preprocess for point-location queries, and where we are given the probability $\\gamma_i$ that the query point lies in a polygon $P_i$ of $\\mathcal{S}$. We show how to preprocess $\\mathcal{S}$ such that the query time for a point~$p\\in P_i$ depends on~$\\gamma_i$ and, in addition, on the distance from $p$ to the boundary of~$P_i$---the further away from the boundary, the faster the query. More precisely, we show that a point-location query can be answered in time $O\\left(\\min \\left(\\log n, 1 + \\log \\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00767","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"}