Why Stable Matchings?

This week we'll develop an algorithm that finds the maximum amount of water which can be routed in a given water supply network. This algorithm is also used in practice for optimization of road traffic and airline scheduling. We'll see how flows in networks are related to matchings in bipartite graphs. We'll then develop an algorithm which finds stable matchings in bipartite graphs. This algorithm solves the problem of matching students with schools, doctors with hospitals, and organ donors with patients. By the end of this week, we'll implement an algorithm which won the Nobel Prize in Economics!

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