# Max flow problem

### From Glossary

In a network, there are two special nodes in
a *source* and a *sink* . The problem is to maximize the
flow from to subject to conservation
of flow constraints at each node and flow bounds on each arc. The max flow labeling algorithm provides a constructive proof of the Max flow - Min cut theorem.

This can also be obtained from the duality of the following linear program:

for ;

for

are upper bounds (capacities) on arc flows, and each sum is for such that the indicated arc is in