Open course ware

We've seen graphs involving boys and girls and connections between them in the context of our sexual demographics calculation and study. A similar problem comes up in terms of what I call stable matching, which is again the issue of matching up boys and girls in a special way according to some constraints. It turns out to have a lot of applications which we'll discuss toward the end. Let's just look at what the problem is. The setup is that there's some number of boys, in this case 5, 1 through 5, and an equal number of girls labeled A through E. And each of the boys has a ranking of the girls. Different rankings, because different boys have different preferences. And likewise, the girls have rankings of the boys. Different girls have different preferences. So here, girl A likes boy 3 best and boy 5 second best, and boy 1 likes girls C best and girl D least. So the problem, basically, is that we want to get all the boys married to all the girls. We want to...