TIGHT BOUNDS ON THE NUMBER OF MINIMUM-MEAN CYCLE CANCELLATIONS AND RELATED RESULTS

We prove a tight Theta(min(nm log(nC), nm(2))) 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(2)). 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(2)) iterations.