Analysis of preflow push algorithms for maximum network flow

Abstract

We study the class of preflow push algorithms recently introduced by Goldberg and Tarjan for solving the maximum network flow problem on a weighted digraph G(V,E). We improve Goldberg and Tarjanis O(n³) time bound for the maximum distance preflow push algorithm to O(n²√m) and show that this bound is tight by constructing a parametrized worst case network. We then develop the maximal excess preflow push algorithm and show that it achieves a bound of O(n²√m) pushes. Based on this we develop a maximum network flow algorithm for the synchronous distributed model of computation that uses at most O(n²√m) messages and O(n²) time, thereby improving upon the best previously known algorithms for this model.