求解最大流问题的matlab程序（Matlab program for solving maximum flow problems）.docVIP

求解最大流问题的matlab程序（Matlab program for solving maximum flow problems） Maximum flow algorithm Algorithm idea: the maximum flow problem is actually a feasible flow {fij}, which makes the V (f) reach the maximum. If you give a feasible flow F, as long as there is no judgment in N augmenting path on the F, if there is an augmented path, improved F, a new feasible flow rate increases; if there is no augmenting path, get the maximum flow. 1. labeling method for maximum flow (Ford, Fulkerson) Starting with a feasible flow (a general zero flow), the following labeling procedure and the adjustment process are followed until no augmenting path about F can be found. (1) labeling process In this process, the points in the network are divided into labeled and unlabeled points, and the labeled points are divided into two kinds: checked and unchecked. Each label label information points are expressed in two parts: the first label show that the label from which point to start the traceback path from the VT to find out is augmented; second label is said to have checked whether the vertex. At the start of the label, mark vs (s, 0), when vs is the label, but at the end of the check point, and the rest are unlabeled points, denoted as (0, 0). Take a label without checking the point VI, for all unlabeled points, vj: A. for arc (VI, VJ), if fijcij, then give the VJ label (VI, 0), then the VJ point becomes the label, which is not checked. B. for arc (VI, VJ), if fji0, then give the VJ label (-vi, 0), then the VJ point becomes the label, which is not checked. Thus, VI becomes a labeled and checked point, and its second label is denoted as 1. Repeat the steps above and, once VT is marked, indicate an extended path from VI to P, and VT into the adjustment process. If all the labels have been checked and the label process fails, the algorithm ends with the feasible flow being the maximum flow. (2) adjustment process From the VT point, through the first label of each point, backward tracing, we c