Network flow problems

* Network or capacity network: Refers to a connected weighted graph d= (v,e), where V is the set of vertices of the graph, and E is a set of forward edges (that is, arcs).

* Stream on the network: is a function f={f (U,V)} that is specified in the ARC set E, and the traffic on the arc (U,V) is called F (u,v).

* In V there is a source point S, a meeting point T, and the flow on the network is the sink point from which the source point flows out eventually.

* Each forward edge (U,V) in E has a corresponding capacity limit of C (u,v), and the flow through this edge cannot exceed the upper limit.

* The total incoming stream must be equal to the total emitted stream at any vertex v that is neither the source point nor the sink point. The maximum flow problem is to determine the maximum amount of traffic that can be passed from S to T.

Network flow problems