VERTEX ENUMERATION OF POLYHEDRA

ABSTRACT

The vertex enumeration problem of a polyhedron P in ℜⁿ , 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 $O\left(m{\left(m+n\right)}^{2\times min\left\{m,n\right\}}\right)$ which is $O\left(mn\left|V\left(P\right)\right|\right)$ for the case of non-degenerate polyhedra, where $\left|V\left(P\right)\right|$ 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.

Keywords:
vertex enumeration; polyhedra; pivoting