Chapter 22. Network Flow

Graphs, digraphs, and networks are just mathematical abstractions, but they are useful in practice because they help us to solve numerous important problems. In this chapter, we extend the network problem-solving model to encompass a dynamic situation where we imagine material flowing through the network, with different costs attached to different routes. These extensions allow us to tackle a surprisingly broad variety of problems with a long list of applications.

We see that these problems and applications can be handled within a few natural models that we can relate to one another through reduction. There are several different ways, all of which are technically equivalent, to formulate the basic problems. To implement ...

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