{"paper":{"title":"Computing the Approximate Convex Hull in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"cs.CG","authors_text":"Hossein Sartipizadeh, Tyrone L. Vincent","submitted_at":"2016-03-08T22:20:02Z","abstract_excerpt":"In this paper, an effective method with time complexity of $\\mathcal{O}(K^{3/2}N^2\\log \\frac{K}{\\epsilon_0})$ is introduced to find an approximation of the convex hull for $N$ points in dimension $n$, where $K$ is close to the number of vertices of the approximation. Since the time complexity is independent of dimension, this method is highly suitable for the data in high dimensions. Utilizing a greedy approach, the proposed method attempts to find the best approximate convex hull for a given number of vertices. The approximate convex hull can be a helpful substitute for the exact convex hull "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04422","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"}