Algorithm 9-1: Maximum Flow and minimum cut

Minimum Cut Problem

First, we will introduce what cutting is. Cutting is to divide the vertices in a graph into two parts: A and B.

Next we will introduce what capacity is. Capacity is the sum of edge weights from Area A to area B.

The minimum cutting method is to find a graph to minimize the capacity.

Minimum Cut Application

Minimum cutting is used in country splitting. The famous Soviet collapse event is to achieve national split through the smallest cut of computing. During modeling, the city is used as the vertex in graph theory and the railway is used as the edge between the vertices. Finally, the national border is defined by calculating the minimum cut.

Maximum Flow Problems

The maximum flow is the maximum traffic supported by the network from vertex s to vertex T through all edges. Vertex t receives traffic from three directions. The sum of the traffic is 28, so the maximum flow is 28.