h1_sol_r

h1_sol_r - CSE 202 Homework 1 Solution(Revised TA Nan Zang...

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CSE 202 Homework 1 Solution (Revised 1/21/2008) TA: Nan Zang Note these are only sketch answers , not full answers. Problem 1 Solution: False Counter example: Two men {m,m’}. Two women {w,w’} m prefers w to w’ m’ prefers w’ to w w prefers m’ to m w’ prefers m to m’. There are two stable matchings: 1. m Ù w’ and m’ Ù w 2. m Ù w and m’ Ù w’. None of them satisfy the condition described by the problem. Problem 2: Solution True Explanation We know w is ranked first in m’s preference list and m is ranked first in w’s preference list. Assume pair (w, m) is not in the stable matching, then w is paired with some other man m’ and m is paired with some other women: m Ù w’ and m’ Ù w. However, m prefers w to its current partner w’ and w prefers m to its current partner m’, which is a contradiction with the definition of stable matching. Problem 3: Solution (b) There are four tv shows total, each station has two. The four tv shows have rating 1, 2, 3, 4 separately:
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This note was uploaded on 05/21/2008 for the course CS CO453 taught by Professor Graham during the Winter '08 term at UCSD.

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h1_sol_r - CSE 202 Homework 1 Solution(Revised TA Nan Zang...

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