{"paper":{"title":"Asymmetric Convex Intersection Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Luis Barba, Wolfgang Mulzer","submitted_at":"2018-08-20T14:14:45Z","abstract_excerpt":"We consider asymmetric convex intersection testing (ACIT).\n  Let $P \\subset \\mathbb{R}^d$ be a set of $n$ points and $\\mathcal{H}$ a set of $n$ halfspaces in $d$ dimensions. We denote by $\\text{ch}(P)$ the polytope obtained by taking the convex hull of $P$, and by $\\text{fh}(\\mathcal{H})$ the polytope obtained by taking the intersection of the halfspaces in $\\mathcal{H}$. Our goal is to decide whether the intersection of $\\mathcal{H}$ and the convex hull of $P$ are disjoint. Even though ACIT is a natural variant of classic LP-type problems that have been studied at length in the literature, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06460","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"}