AN O(N2(M+NLOGN)LOGN) MIN-COST FLOW ALGORITHM

The minimum cost flow problem is: Given a network with n vertices and m edges, find a maximum flow of minimum cost. Many network problems are easily reducible to this problem. A polynomial-time algorithm for the problem has been known for some time, but only recently a strongly polynomial algorithm was discovered. In this paper an O(n**2(m plus n log n)log n) algorithm is designed. The previous best algorithm, due to Fujishige and Orlin, had an O(m**2(m plus n log n)log n) time bound. Thus, for dense graphs an improvement of two orders of magnitude is obtained. The algorithm in this paper is based on Fujishige's algorithm (which is based on Tardos's algorithm).