Efficiency of the Network Simplex Algorithm for the Maximum Flow Problem
Goldfarb and Hao have proposed a network simplex algorithm that will solve a maximum flow problem on an n-vertex, m-arc network in at most nm pivots and O(n2m) time. In this paper we describe how to implement their algorithm to run in O(nm log n) time by using an extension of the dynamic tree data
structure of Sleator and Tarjan. This bound is less than a logarithmic factor larger than that of any other known algorithm for the problem.