Flow Network Capacity Augmentation

[mXSCNT]

Suppose that you have a http://en.wikipedia.org/wiki/Flow_network" with integer edge capacities, and n dollars. You may spend one dollar to increase the capacity of an existing edge by one. The question is, how can you spend your dollars so that the maximum flow through the resulting network is maximized?

 

[bpet]

Suppose that you have a http://en.wikipedia.org/wiki/Flow_network" with integer edge capacities, and n dollars. You may spend one dollar to increase the capacity of an existing edge by one. The question is, how can you spend your dollars so that the maximum flow through the resulting network is maximized?

The max-flow min-cut theorem might be a good place to start in constructing a spending strategy.