{"paper":{"title":"Finding Efficient Region in The Plane with Line segments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Jack Wang","submitted_at":"2012-10-29T12:27:18Z","abstract_excerpt":"Let $\\mathscr O$ be a set of $n$ disjoint obstacles in $\\mathbb{R}^2$, $\\mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $\\mathscr M$, respectively. Given a point $p$ in ${R}^2$, we say the point $p$ is achievable for $\\mathscr M$ such that $\\pi(s,p)\\leq l$, where $\\pi(\\cdot)$ denotes the shortest path length in the presence of obstacles. One is to find a region $\\mathscr R$ such that, for any point $p\\in \\mathbb{R}^2$, if it is achievable for $\\mathscr M$, then $p\\in \\mathscr R$; otherwise, $p\\notin \\mathscr R$. In this pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7638","kind":"arxiv","version":10},"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"}