  Computing mixed volume of convex polytopes is an important problem in
computational algebraic geometry. This paper establishes sufficient conditions
under which the mixed volume of several convex polytopes exactly equals the
normalized volume of the convex hull of their union. Under these conditions the
problem of computing mixed volume of several polytopes can be transformed into
a volume computation problem for a single polytope in the same dimension. We
demonstrate through problems from real world applications that substantial
reduction in computational costs can be achieved via this transformation in
situations where the convex hull of the union of the polytopes has less complex
geometry than the original polytopes. We also discuss the important
implications of this result in the polyhedral homotopy method for solving
polynomial systems.
