A new model for multicommodity flow problems, and a strongly polynomial algorithm for single-source Maximum Concurrent Flow

In this paper, a new decomposition approach is proposed to solve large size instances of Multicommodity Flow problems. Instead of generating paths, we generate trees in a convenient way. Numerical results show that the new approach is much more efficient than the classical paths generation approach. Moreover, we propose a combinatorial polynomial-time algorithm to solve the maximum concurrent flow problem (MCF) in the single-source case.