The NW (Newman-Watts) small-world network and the BA (Barabasi-Albert) scale-free network are two kinds of common network in reality, these two kinds of networks have a highly possibility existing multiple paths between any pair of vertexes. If abandoning saturated augmented chain and finding augmented chain, the efficiency is not high. The fact above urged a high performance new algorithm described as minimum cut/maximum flow algorithm based on augmenting path restoration to manage these two networks. The new algorithm constantly sought vertexes following greedy heuristics to restore saturated augmenting paths which generated by adjusting flow on shortest paths. By experimental comparisons on the NW small-world network and the BA scale-free network, the new algorithm was several times faster than Ford-Fulkerson algorithm and half as Dinic algorithm in RAM usage, as a consequence, the new algorithm was capable of calculating growing telecommunication and traffic networks.

Aiming at the problem of the low execution efficiency in the part of the network caused by the backtracking phenomena of the original highest label preflow push algorithm, the lowest label algorithm based on preflow push was proposed. Based on the preflow, the proposed algorithm chose the lowest label active node as the adjustment point in the selection of active nodes by following the greedy algorithm. The backtracking verification method was introduced to terminate the backtracking loop for enhancing the efficiency of algorithm. The proposed algorithm could meet the demands of various kinds of network graphs and was five more times faster than the classic highest label preflow push algorithm for the sparse networks in the simulation experiments. When applied into the image segmentation, the proposed method achieved more than 50 percent of speed compared with the classic algorithm. The proposed lowest label algorithm for minimum cut/maximum flow based on preflow push can satisfy the large-scale network traffic distribution and the image processing of computer vision.