Algorithm 9-3: Theory of maximum flow and minimum cut

This topic describes the relationship between the maximum flow problem and the minimum cut problem. In fact, these two problems are equivalent.

Now we divide a network into two parts: A and B. We define the net flow traffic crossover SS between A and B) that is, the maximum traffic from A to B minus the maximum traffic from B to.

Next we will introduce flow-value lemma ). If F is any stream in the network and (A, B) is any cutting method of the network, then (A, B) the net traffic crossover is equivalent to the Traffic Value of F. The flow value theorem is displayed.

Let's explain it in plain words. First, cut the network into two parts A and B, then the traffic between AB is the total traffic from A to B minus the total traffic from B to.

The minimum traffic in the least cut problem refers to the traffic in the above flow value theorem.

The minimum cut problem can be converted to the maximum flow problem. That is to say, the minimum cut can be calculated from the maximum flow chart. The calculation steps are as follows. First, starting from the origin S, we will regard the forward path with full capacity and the reverse path with empty capacity as obstacles. Starting from the origin, we will traverse all the reachable vertices. The final vertex that can be reached is the minimum cut.