{"paper":{"title":"Robust Vertex Enumeration for Convex Hulls in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Bahman Kalantari, Pranjal Awasthi, Yikai Zhang","submitted_at":"2018-02-05T17:13:16Z","abstract_excerpt":"Computation of the vertices of the convex hull of a set $S$ of $n$ points in $\\mathbb{R} ^m$ is a fundamental problem in computational geometry, optimization, machine learning and more. We present \"All Vertex Triangle Algorithm\" (AVTA), a robust and efficient algorithm for computing the subset $\\overline S$ of all $K$ vertices of $conv(S)$, the convex hull of $S$. If $\\Gamma_*$ is the minimum of the distances from each vertex to the convex hull of the remaining vertices, given any $\\gamma \\leq \\gamma_* = \\Gamma_*/R$, $R$ the diameter of $S$, $AVTA$ computes $\\overline S$ in $O(nK(m+ \\gamma^{-2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01515","kind":"arxiv","version":2},"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"}