sol1 - CSE 202 Solution Set 1 Spring 2010 7 April 2010...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CSE 202 Solution Set 1 Spring 2010 7 April 2010 Chapter 1, Problem 1: The statement is false, which is evident due to the following counterexample with 2 men ( m 1 and m 2 ) and 2 women ( w 1 and w 2 ). The preferences are as follows: • m 1 prefers w 1 to w 2 , • m 2 prefers w 2 to w 1 , • w 1 prefers m 2 to m 1 , and • w 2 prefers m 1 to m 2 . A stable matching in this instance is { ( m 1 ,w 1 ) , ( m 2 ,w 2 ) } . Note that this matching does not include a pair ( m,w ) where m and w are ranked first on each other’s preference list. Chapter 1, Problem 2: The statement is true, which can be proved by contradiction. Suppose that the Gale-Shapley algorithm returns a stable matching where m and w are not matched, but they are first on each other’s preference lists. This means that m is matched with some other woman w , and w is matched with some other woman m . But the preference lists imply that m prefers w to w , and w prefers m to m . This is an instability, which contradicts the fact that the Gale-Shapley algorithm always returns a stable matching. Therefore, ( m,w ) must be included in the matching. Chapter 1, Problem 4: We give the following algorithm that matches students to hospitals. Then algo- rithm and its analysis are every similar to the original Gale-Shapley algorithm for the stable matching problem: Initially all students s ∈ S and hospital positions h ∈ H are free While there is a hospital h that has a free position and hasn’t extended an offer to every student: Choose such a hospital h Let s be the highest-ranked student in h ’s preference list that hasn’t received an offer from...
View Full Document

This note was uploaded on 04/20/2010 for the course CSE 202 taught by Professor Hu during the Spring '06 term at UCSD.

Page1 / 2

sol1 - CSE 202 Solution Set 1 Spring 2010 7 April 2010...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online