Figure 1: (a) An illustration of a maximum flow problem on a graph. The numbers above the arcs are capacities, and we wish to maximize flow from the source 𝑆 to the sink 𝑇 ; equivalently, we wish to maximize flow along the artificial arc ( 𝑇 , 𝑆 ) such that the flow at each node is balanced. (b) An example of a small maximum flow problem with a gap such that no flow along arc ( 𝑇 , 𝑆 ) is possible.