Polynomial dual network simplex algorithms

The authors show how to use polynomial and strongly polynomial capacity scaling algorithms for the transshipment problem to design a polynomial dual network simplex pivot rule. The present best pivoting strategy leads to an O(m²logn) bound on the number of pivots, where n and m denotes the number of nodes and arcs in the input network. If the demands are integral and at most B, the authors also give an O(m(m+nlogn)min(lognB,mlogn))-time implementation of a strategy that requires somewhat more pivots.