The Pseudoflow Algorithm and the Pseudoflow-Based Simplex for the Maximum Flow Problem

We introduce an algorithm that solves the maximum ow problem without generating ows explicitly The algorithm solves di rectly 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 pseudo ow 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 pseudo ow algorithm the new simplex algo rithm and the parametric analysis for both algorithms are O mn log n on a graph with n nodes and m arcs