# Hw1s - 2 Decide whether you think the following statement is true or false If true give a short explanation If false give a counter-example

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CSci 570 Homework set #1 Solution Instructor: Prof. Shamsian Due on September 14th 1. Decide whether you think the following statement is true or false. If true, give a short explanation. If false, give a counter-example. “In every instance of the Stable Matching Problem there is a stable matching containing a pair (m,w) such that m is ranked first by w, and w is ranked first by m.” Solution: False. Suppose that we have two men m0, m1 and two women w0, w1. Let m0 rank w0 first, w0 rank m1 first, m1 rank w1 first and w1 rank m0 first. We see that such a pair as described by the claim does not exist.
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Unformatted text preview: 2. Decide whether you think the following statement is true or false. If true, give a short explanation. If false, give a counter-example. “Consider an instance of the Stable Matching Problem in which there exists a man m and a woman w such that m is ranked first by w, and w is ranked first by m. Then (m,w) must appear in every stable matching.” Solution: True. Suppose S is a stable matching that contains the pairs (m, w0) and (m0, w), for some m0, w0. However, clearly, (m, w) forms an instability pair, contradicting the stability of S....
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## This note was uploaded on 01/22/2010 for the course CSCI 570 taught by Professor Shamsian during the Fall '06 term at USC.

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