Find a stable marriage matching for the instance given in the picture by applying the stable marriage algorithm a. in its men-proposing version. b. in its women-proposing version.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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 Find a stable marriage matching for the instance given in the picture by applying the stable marriage algorithm

a. in its men-proposing version.

b. in its women-proposing version.

Consider an instance of the stable marriage problem given by the following
ranking matrix:
α
B
Y
A
B C
1,3 2,2
3,1
3,1 1,3 2,2
2,2 3,1
1,3
Transcribed Image Text:Consider an instance of the stable marriage problem given by the following ranking matrix: α B Y A B C 1,3 2,2 3,1 3,1 1,3 2,2 2,2 3,1 1,3
Stable marriage algorithm
Input: A set of n men and a set of n women along with rankings of the women
by each man and rankings of the men by each woman with no ties
allowed in the rankings
Output: A stable marriage matching
Step 0 Start with all the men and women being free.
Step 1 While there are free men, arbitrarily select one of them and do the
following:
Proposal The selected free man m proposes to w, the next
woman on his preference list (who is the highest-ranked woman
who has not rejected him before).
Response If w is free, she accepts the proposal to be matched
with m. If she is not free, she compares m with her current mate. If
she prefers m to him, she accepts m's proposal, making her former
mate free; otherwise, she simply rejects m's proposal, leaving m
free.
Step 2 Return the set of n matched pairs.
Transcribed Image Text:Stable marriage algorithm Input: A set of n men and a set of n women along with rankings of the women by each man and rankings of the men by each woman with no ties allowed in the rankings Output: A stable marriage matching Step 0 Start with all the men and women being free. Step 1 While there are free men, arbitrarily select one of them and do the following: Proposal The selected free man m proposes to w, the next woman on his preference list (who is the highest-ranked woman who has not rejected him before). Response If w is free, she accepts the proposal to be matched with m. If she is not free, she compares m with her current mate. If she prefers m to him, she accepts m's proposal, making her former mate free; otherwise, she simply rejects m's proposal, leaving m free. Step 2 Return the set of n matched pairs.
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