The Pseudo ow Algorithm and thePseudo ow - Based Simplex for

We introduce an algorithm that solves the maximum ow problem without generating ows explicitly. The algorithm solves directly a problem we call the maximum s-excess problem. That problem is equivalent to the minimum cut problem, and is a direct extension of the maximum closure problem. The concepts used also lead to a new parametric analysis algorithm generating all breakpoints in the amount of time of a single run. The insights derived from the analysis of the new algorithm lead to a new simplex algorithm for the maximum ow problem { a pseudooow-based simplex. We show that this simplex algorithm can perform a parametric analysis in the same amount of time as a single run. This is the rst known simplex algorithm for maximum ow that generates all possible breakpoints of parameter values in the same complexity as required to solve a single maximum ow instance and the fastest one. The complexities of our pseudooow algorithm, the new simplex algorithm , and the parametric analysis for both algorithms are O(mn log n) on a graph with n nodes and m arcs.