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MIT6_042JF10_rec07

# MIT6_042JF10_rec07 - 6.042/18.062J Mathematics for Computer...

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6.042/18.062J Mathematics for Computer Science October 1, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 7 1 A Protocol for College Admission Next, we are going to talk about a generalization of the stable marriage problem. Recall that we have some horses and we’d like to pair them with stables so that there is no incentive for two horses to swap stables. Oh wait, that’s a different problem. The problem we’re going to talk about is a generalization of the one done in lecture. In the new problem, there are N students s 1 , s 2 , . . . , s N and M universities u 1 , u 2 , . . . , u M . M University u i has n i slots for students, and we’re guaranteed that i =1 n i = N . Each student ranks all universities (no ties) and each university ranks all students (no ties). Design an algorithm to assign students to universities with the following properties 1. Every student is assigned to one university. 2. i , u i gets assigned n i students.

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