Note on the complexity of the mixed-integer hull of a polyhedron

We study the complexity of computing the mixed-integer hull View the MathML source of a polyhedron P. Given an inequality description, with one integer variable, the mixed-integer hull can have exponentially many vertices and facets in d. For n,d fixed, we give an algorithm to find the mixed-integer hull in polynomial time. Given a finite set V⊆Qn+d, with n fixed, we compute a vertex description of the mixed-integer hull of View the MathML source in polynomial time and give bounds on the number of vertices of the mixed-integer hull. Keyword