CMPSC360hw4 - CMPSC 360 Discrete Mathematics for Computer...

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Unformatted text preview: CMPSC 360 Discrete Mathematics for Computer Science, Fall 2008 Homework 4 Out: Sept. 18, Due: Sept. 25 by 5:00pm Instructions: Write your name, section number and CMPSC 360 on your assignments. Put your solutions in the homework box in 342G by 5pm on Thursday. 1. Man-optimal, Woman-optimal In a particular instance of the stable marriage problem with n men and n women, it turns out that there are exactly three distinct stable matchings, M 1 , M 2 , M 3 . Also, each woman W has a different partner in the three matchings. Therefore each woman has a clear preference ordering of the three matchings (according to the ranking of her partners in her preference list). Now, suppose for woman W 1 , this order is M 1 > M 2 > M 3 . True or false: every woman has the same preference ordering M 1 > M 2 > M 3 . Justify your answer. 2. College Admissions In the College Admissions Problem, we are given n students and m universities. Each university j has some number, q j , of slots, and we assume that the total number of...
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CMPSC360hw4 - CMPSC 360 Discrete Mathematics for Computer...

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