{"paper":{"title":"Faster and More Robust Mesh-based Algorithms for Obstacle k-Nearest Neighbour","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Daniel D. Harabor, David Taniar, Shizhe Zhao","submitted_at":"2018-08-13T02:05:27Z","abstract_excerpt":"We are interested in the problem of finding $k$ nearest neighbours in the plane and in the presence of polygonal obstacles ($\\textit{OkNN}$). Widely used algorithms for OkNN are based on incremental visibility graphs, which means they require costly and online visibility checking and have worst-case quadratic running time. Recently $\\mathbf{Polyanya}$, a fast point-to-point pathfinding algorithm was proposed which avoids the disadvantages of visibility graphs by searching over an alternative data structure known as a navigation mesh. Previously, we adapted $\\mathbf{Polyanya}$ to multi-target s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04043","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"}