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Chapter 10: Matchings, Cuts, and Flows. How do you match, say, students with colleges so you maximize total 
satisfaction? In an online community, how do you know whom to trust? And how do you find the total capacity of a 
road network? These, and several other problems, can be solved with a small class of closely related algorithms and 
are all variations of the maximum flow problem, which is covered in this chapter.

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Chapter 1 
■
 IntroduCtIon
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Chapter 11: Hard Problems and (Limited) Sloppiness. As alluded to in the beginning of the introduction, there are 
problems we don’t know how to solve efficiently and that we have reasons to think won’t be solved for a long time—
maybe never. In this chapter, you learn how to apply the trusty tool of reduction in a new way: not to solve problems 
but to show that they are hard. Also, we take a look at how a bit of (strictly limited) sloppiness in the optimality criteria 
can make problems a lot easier to solve.