{"paper":{"title":"Computing the Minkowski Sum of Convex Polytopes in $\\Re^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Sandip Das, Swami Sarvottamananda","submitted_at":"2018-11-14T14:39:35Z","abstract_excerpt":"We propose a method to efficiently compute the Minkowski sum, denoted by binary operator $\\oplus$ in the paper, of convex polytopes in $\\Re^d$ using their face lattice structures as input. In plane, the Minkowski sum of convex polygons can be computed in linear time of the total number of vertices of the polygons. In $\\Re^d$, we first show how to compute the Minkowski sum, $P \\oplus Q$, of two convex polytopes $P$ and $Q$ of input size $n$ and $m$ respectively in time $O(nm)$. Then we generalize the method to compute the Minkowski sum of $n$ convex polytopes, $P_1 \\oplus P_2 \\oplus \\cdots \\opl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05812","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"}