{"paper":{"title":"On Triangluar Separation of Bichromatic Point Sets in Polygonal Environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Farnaz Sheikhi, Sharareh Alipour","submitted_at":"2018-09-01T05:23:55Z","abstract_excerpt":"Let $\\mathcal P$ be a simple polygonal environment with $k$ vertices in the plane. Assume that a set $B$ of $b$ blue points and a set $R$ of $r$ red points are distributed in $\\mathcal P$. We study the problem of computing triangles that separate the sets $B$ and $R$, and fall in $\\mathcal P$. We call these triangles \\emph{inscribed triangular separators}. We propose an output-sensitive algorithm to solve this problem in $O(r \\cdot (r+c_B+k)+h_\\triangle)$ time, where $c_B$ is the size of convex hull of $B$, and $h_\\triangle$ is the number of inscribed triangular separators. We also study the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00116","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"}