The projected pairwise multicommodity flow polyhedron Original Research Article

The object of this paper is a simple characterization of the vertices and extreme rays of the undirected multicommodity flow polyhedron View the MathML source, which has one variable for each channel. This polyhedron is seen as a linear projection of the high-dimensional directed multicommodity flow polyhedron View the MathML source, which has variables corresponding to each possible tuple of the form (channel, direction, origin, destination). Along with the characterization of vertices and rays of View the MathML source, a computationally verifiable necessary condition for the vertices is given. It is shown that no polynomially bounded analytical description of View the MathML source exists, by exhibiting exponentially many facets of View the MathML source.