Updating maximum flow
Updating the path in the way described here yields the flow shown in Figure 1a.We are left with the following residual network where a path between the source and the sink doesn’t exist: This example suggests the following algorithm: start with no flow everywhere and increase the total flow in the network while there is an augmenting path from the source to the sink with no full forward edges or empty backward edges - a path in the residual network.A cut in a flow network is simply a partition of the vertices in two sets, let’s call them A and B, in such a way that the source vertex is in A and the sink is in B.
We are asked to associate another value f satisfying f â‰¤ c for each edge such that for every vertex other than the source and the sink, the sum of the values associated to the edges that enter it must equal the sum of the values associated to the edges that leave it. Furthermore, we are asked to maximize the sum of the values associated to the arcs leaving the source, which is the total flow in the network.
The simplest form that the statement could take would be something along the lines of: “A list of pipes is given, with different flow-capacities. What is the maximum amount of water that you can route from a given starting point to a given ending point?