Stable marriage problem: Difference between revisions

Content added Content deleted

Inline

@@ Line 4: / Line 4: @@
 '''Problem description'''<br>
-Given an equal number of men and women to be paired for marriage, each man ranks all the women in order of his preference and each women ranks all the men in order of her preference.
+Given an equal number of men and women to be paired for marriage, each man ranks all the women in order of his preference and each woman ranks all the men in order of her preference.
-A stable set of engagements for marriage is one where no man prefers a women over the one he is engaged to, where that other woman ''also'' prefers that man over the one she is engaged to. I.e. with consulting marriages, there would be no reason for the engagements between the people to change.
+A stable set of engagements for marriage is one where no man prefers a woman over the one he is engaged to, where that other woman ''also'' prefers that man over the one she is engaged to. I.e. with consulting marriages, there would be no reason for the engagements between the people to change.
 Gale and Shapley proved that there is a stable set of engagements for any set of preferences and the first link above gives their algorithm for finding a set of stable engagements.