Vertex Enumeration of Polyhedra

Abstract

The vertex enumeration problem of a polyhedron P in ℜ n , given by m inequalities, is widely discussed in the literature. In this work it is introduced a new algorithm to solve it. The algorithm is based on lexicographic pivoting and the worst-case time complexity is O m (m + n) 2×min{m,n} , which is O (mn |V (P)|) for the case of non-degenerate polyhedra, where |V (P)| is the number of vertices of P. The proposed algorithm was coded in Matlab and numerical experiments performed for several randomly generated problems show its efficiency.