A polynomial time algorithm for solving the maximum flow problem in directed networks

An efficient polynomial time algorithm for solving maximum flow problems has been proposed in this paper. The algorithm is basically based on the binary representation of capacities; it solves the maximum flow problem as a sequence of O(m) shortest path problems on residual networks with nodes and m arcs. It runs in O(m²r) time, where is the smallest integer greater than or equal to log B , and B is the largest arc capacity of the network. A numerical example has been illustrated using this proposed algorithm.(author)