Decomposition and parallelization techniques for enumerating the facets of combinatorial polytopes

A convex polytope can either be described as convex hull of vertices or as solution set of a finite number of linear inequalities and equations. Whereas both representations are equivalent from a theoretical point of view, they are not when optimization problems over the polytope have to be solved. It is a challenging task to convert one description into the other. In this paper we address the efficient computation of the facet structure of several polytopes associated with combinatorial optimization problems. New results axe presented which are of interest for theoretical investigations as well as for practical optimization.