A deficit scaling algorithm for the minimum flow problem

In this paper, we develop a new preflow algorithm for the minimum flow problem, called deficit scaling algorithm, This is a special implementation of the generic preflow algorithm for the minimum How problem developed by Ciurea and Ciupala earlier. The bottleneck operation in the generic preflow algorithm is the number of noncancelling pulls. Using the scaling technique (i.e. selecting the active nodes with sufficiently large deficits), we reduce the number of noncancelling pulls to O(n(2) log (c) over bar) and obtain an O(nm + n(2) log (c) over bar) algorithm.