Tight bounds on the number of minimum-mean cycle cancellations and related results.

We prove a tight Θ(min( nm log(nC), nm)) bound on the number of iterations of the minimum-mean cycle-canceling algorithm of Goldberg and Tarjan [13]. We do this by giving the lower bound and by improving the strongly polynomial upper bound on the number of iterations to O(nm). We also give an improved version of the maximum-mean cut canceling algorithm of [7], which is a dual of the minimum-mean cycle-canceling algorithm. Our version of the dual algorithm runs in O(nm) iterations. [ABSTRACT FROM AUTHOR]