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Aug 22, 2019 at 17:17 vote accept Jack
Aug 22, 2019 at 16:54 comment added Neil Slater @Jack: That may work as a variation of the initial greedy algorithm. You will still need some kind of refinement stage if you want to get closer to fully optimised. How much of difference there is between an initial greedy algorithm and the improvements possible through local search depends very much on your data.
Aug 22, 2019 at 15:54 comment added Jack Awesome! Your idea inspired another thought: Apologies for the sexism. This is not my real use case. What if for each man, I record their top N women. Then I match every man with their top woman, ignoring potential polygamy. Then for each woman, if she is matched with multiple men, I match the "less optimal" man with his second choice woman, again ignoring potential polygamy.
Aug 22, 2019 at 8:42 history edited Neil Slater CC BY-SA 4.0
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Aug 22, 2019 at 8:29 history answered Neil Slater CC BY-SA 4.0