{"paper":{"title":"Adaptive Planar Point Location","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Man-Kit Lau, Siu-Wing Cheng","submitted_at":"2018-10-01T14:17:40Z","abstract_excerpt":"We present self-adjusting data structures for answering point location queries in convex and connected subdivisions. Let $n$ be the number of vertices in a convex or connected subdivision. Our structures use $O(n)$ space. For any convex subdivision $S$, our method processes any online query sequence $\\sigma$ in $O(\\mathrm{OPT} + n)$ time, where $\\mathrm{OPT}$ is the minimum time required by any linear decision tree for answering point location queries in $S$ to process $\\sigma$. For connected subdivisions, the processing time is $O(\\mathrm{OPT} + n + |\\sigma|\\log(\\log^* n))$. In both cases, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00715","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"}