{"paper":{"title":"An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.RO"],"primary_cat":"cs.CG","authors_text":"Kyle Fox, Oren Salzman, Pankaj K. Agarwal","submitted_at":"2017-06-09T13:11:37Z","abstract_excerpt":"We study a path-planning problem amid a set $\\mathcal{O}$ of obstacles in $\\mathbb{R}^2$, in which we wish to compute a short path between two points while also maintaining a high clearance from $\\mathcal{O}$; the clearance of a point is its distance from a nearest obstacle in $\\mathcal{O}$. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let $n$ be the total number of obstacle vertices and let $\\varepsilon \\in (0,1]$. Our algorithm computes i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02939","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"}