Minkowski addition of convex polytopes

Abstract

This note summarizes recent results from computational geometry which determine complexity of computing Minkowski sum of k convex polytopes in R d, which are represented either in terms of facets or in terms of vertices. In particular, it is pointed out for which cases there exists an algorithm which runs in polynomial time. The note is based on papers of Gritzmann and Sturmfels [6] and Komei Fukuda [3]. An algorithm which aims at reducing the complexity of obtaining minimal representation of polytopes given by a set of inequalities is presented as well