For those (like me) who clicked because algorithms are fun but don't know the max flow problem specifically: http://en.wikipedia.org/wiki/Maximum_flow_problem

TL;DR: what's the fastest way to transport a large amount of data over a mesh of many small pipes

As someone who knows little about this problem or the laws of physics, I wonder if it could be solved using physics -- set up a series of physical pipes, pump water from A to B, measure the flow at each point? If that would work, how complicated would the mesh need to be that solving it with physics is faster than brute-force computation?