Basic Network Flow knowledge

I read a little network stream some time ago. Unfortunately, every summary is written. Every review, so I will try again today... Thank you for your summary.

Several Basic concepts:

1) Residual Network: a Flow Network Graph G = (V, E), under the condition that the capacity of C (u, v) is not exceeded, the additional network traffic that can be pushed between node u and node v is (u, v)Residual capacity.

CF (u, v) = C (u, v)-f (u, v );(F (u, v) is the additional traffic that can be pushed in between u and v)

The new stream network G' = (V, E) composed of these residual capacities is the residual network.

To put it bluntly, some traffic has been pushed in, consuming part of the Capacity of C (u, v), and the remaining capacity is the residual network.

B) residual network:

 

2 ),Augmented path: A simple path from S to T is known for a network G = (V, E) and a stream F. The augmented path P is the residual network G. Without violating the edge capacity limit, each edge (u, v) in the augmented path can accommodate an additional positive network stream from u to v. The path P marked with a black line is an augmented path.

3 ),Network Flow cut: The cut (S, T) diameter V of the stream network G = (V, E) is divided into S and T = V-s. MakeS ε S,T ε T. If F is a stream, the net stream that passes through the cut (S, T) is defined as F (S, T ). The cut (S, T) capacity is C (S, T ). A network flowMinimum CutIt is also the minimum capacity of all cut types.

4 ),Max flow least cut Theorem:

IfFIs a flow in a flow networkG= (V,E) With sourceSAnd sinkT, Then the following conditions are equivalent:

1. FIs a maximum flow inG.

2. The residual networkGFContains no augmenting paths.

3. |F| =C(S,T) For some cut (S,T)G.