Solution of network flow problem with upper and lower bounds of traffic

Before the network flow problem, each arc of the capacity of the lower limit is 0, the upper limit is C. In the network flow problem with the upper and lower bounds of traffic, each arc has a low bound of traffic and an upper bound up.

For such a problem, there are generally three categories:

1. Maximum flow problem with upper and lower bounds without source point and sink point

2. The network maximum flow problem with the upper and lower bounds of the active point and the sink point

3. The network minimum flow problem with the upper and lower bounds of the active point and the sink point

The first type of question:

(No network maximum flow problem with upper and lower bounds of source and sink points)

"1" We need to construct an accompanying network, first to create an additional source point SS and an additional sink point TT;

"2" for each vertex vi in the original network, add a new arc <vi,tt> in the accompanying network, and the capacity is set to the sum of the lower bound of all arcs starting from vertex Vi in the original network;

"3" For each vertex vi in the original network, add a new arc <ss,vi> in the accompanying network, and the capacity is set to the sum of the lower bound of all arcs entering vertex Vi in the original network;

"4" The original network of each arc in the accompanying network is still retained, but the capacity of the arc is set to Up-low;

"5" in the accompanying network, from the additional source point SS to the additional sink point TT runs once the network maximum stream;

If the arc of the additional source point SS is fully loaded, the original network has a feasible flow and jumps to "6";

If the arc emitted by the additional source point SS is not fully loaded, there is no feasible flow in the original network and the algorithm ends;

"6" The maximum flow of the original network when the flow of each arc is accompanied by the network of Arc flow plus the lower limit of the arc, the algorithm ends.

On this question, the bare topic is SGU-194 code see: http://www.cnblogs.com/zufezzt/p/4681043.html

About the latter two kinds of questions, still in the study .....

Solution of network flow problem with upper and lower bounds of traffic