Network Flow

The bipartite matching problem can be generalized quite a bit.

A beautiful generalization is network flow. We'd like to move water (or packets or trucks or...) from one place to another.

• source: A place where water comes from. Source is inexhaustible.
• sink: A place where water needs to go. Sink is insatiable.
• nodes: Junctions along the way from source to sink.
• edges: Carry the water from junction to junction.
• capacities: The size of the pipes (edges) between junctions.
• flow: The amount of water moving through each pipe. Flow is conserved.

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