Synthesis of directed multicommodity flow networks

Abstract A necessary condition for synthesis of multicommodity flow networks is derived. The feasible flow region of a multicommodity flow network is shown to be an antiblocking polyhedron with rational slopes. Also, it is established that this condition is sufficient for two‐commodity flow networks. A synthesis algorithm for two‐commodity flow networks is proposed. The size of the resulting networks is studied and for some regions it is shown to be pseudolinear; in the worst case the network found by the algorithm is optimal to within a constant factor.