A Primal Simplex Algorithm that Solves the Maximum Flow Problem in at most nm Pivots and O(n2m) Time

We propose a primal network simplex algorithm for solving the max imum flow problem which chooses as the arc to enter the basis one that is closest to the source node from amongst all possible candidates. We prove that this algorithm requires at most nm pivots to solve a problem with n nodes and m arcs, and give implementat ions of it which run in O(nZm) time. Our algorithm is, as far as we know, the first strongly polynomial primal simplex algorithm for solving the max imum flow problem.