A Survey of the Stable Marriage Problem and Its Variants

@article{Iwama2008ASO,
  title={A Survey of the Stable Marriage Problem and Its Variants},
  author={Kazuo Iwama and Shuichi Miyazaki},
  journal={International Conference on Informatics Education and Research for Knowledge-Circulating Society (icks 2008)},
  year={2008},
  pages={131-136}
}
  • K. Iwama, S. Miyazaki
  • Published 17 January 2008
  • Economics
  • International Conference on Informatics Education and Research for Knowledge-Circulating Society (icks 2008)
The stable marriage problem is to find a matching between men and women, considering preference lists in which each person expresses his/her preference over the members of the opposite gender. The output matching must be stable, which intuitively means that there is no man- woman pair both of which have incentive to elope. This problem was introduced in 1962 in the seminal paper of Gale and Shapley, and has attracted researchers in several areas, including mathematics, economics, game theory… 

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References

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By exploiting the structure of the set of all stable matchings, and using graph-theoretic methods, an O(n4) algorithm for this problem is derived and achieves the objective of maximizing the average “satisfaction” of all people.

Complexity of the sex-equal stable marriage problem

A stable marriage problem of sizen involvesn men andn women each with a strict preference ordering over all the members of the opposite sex. A solution, called a stable matching, matches the men and

Hard variants of stable marriage

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TLDR
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