An Improved Flow Deviation Method for the Maximum Concurrent Flow Problem

The maximum concurrent flow problem (MCFP) is a multicommodity flow problem in which every pair of vertices can send and receive flow concurrently. The objective of MCFP is to find a maximum throughput and the flow corresponding to the throughput under a set of capacity constraints. We present an improved version of the Flow Deviation Method for the maximum concurrent flow problem, which was first presented by Daniel Bienstock and Olga Raskina in 2000. The algorithm is based on linear programming formulation involving Frank-Wolfe procedure and minimum-cost flow problem. The correctness of the algorithm is strictly proved and the performance is evaluated under several networks of different sizes.