Updating maximum flow
The reader is advised to read the article on graph theory first, as the concepts presented there are needed to understand those presented here.
You are given the one-way roads that connect pairs of cities in the country, and the maximum number of trucks that can drive along each road.
What is the maximum number of trucks that the company can send to the distribution center?
The amount by which this operation can be performed is limited by the capacities of all edges along the path (as shown in Figure 3b).
Once again we take the minimum, to conclude that this path also has capacity 1.
Increasing the flow along this path with 1 yields the flow below: The value of the current flow is now 2, and as shown in Figure 1, we could do better. Clearly, there is no point in considering the directed paths X_A_C_Y or X_B_D_E_Y as the edges C_Y and X_B, respectively, are filled to capacity.