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Stable Matching Problem
原标题:

I am currently reading an Algorithm s book and came across the Stable Matching Problem. And a question came to mind that I m curious about, but the book doesn t answer. In every SMP is it possible to always have one pair where each prefers the other one the most? Like in the classic marriage example. Is there always a pair that have one women and one man where both rank each other at the top of their preference?

最佳回答

A counter example:

M1 prefers W1.
M2 prefers W2.
W1 prefers M2.
W2 prefers M1.

There is no possible pairing where both members of the pair get their highest preference.

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