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→Solutions for constrained problems: No, that won't work |
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:: Not quite. Alice and Bob might not be each other's first choice, but their marriage needs to remain stable given the pairings we find for the rest of the people. In particular, each man that Alice likes better than Bob needs to be paired with a woman he likes better than Alice, ''and'' each woman that Bobs likes better than alice must be paired with a man she likes better than Bob. One can construct examples where this combined condition holds neither for the male-optimal nor for the female-optimal pairing of for the rest ignoring Alice and Bob, but still is possible for some ''third'' stable pairing. [[User:Henning Makholm|Henning Makholm]] 14:05, 26 October 2006 (UTC)
::: So couldn't you just exclude the four persons, do the GS algorithm and then check if the pairings are still stable? Computationally, that would still be in O(m*n). --[[User:Kraymer|Kraymer]] ([[User talk:Kraymer|talk]]) 14:34, 7 February 2010 (UTC)
:::: No; see the last sentence in my 26 October comment. –[[User:Henning Makholm|Henning Makholm]] ([[User talk:Henning Makholm|talk]]) 02:50, 22 October 2010 (UTC)
== Choices of methaphorical gender ==
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