Three fast algorithms for four problems in stable marriage
SIAM Journal on Computing
An efficient algorithm for the “optimal” stable marriage
Journal of the ACM (JACM)
A further note on the stable matching problem
Discrete Applied Mathematics
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Cheating by men in the gale-shapley stable matching algorithm
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Generalized scoring rules and the frequency of coalitional manipulability
Proceedings of the 9th ACM conference on Electronic commerce
Algorithms for the coalitional manipulation problem
Artificial Intelligence
Nonexistence of voting rules that are usually hard to manipulate
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Junta distributions and the average-case complexity of manipulating elections
Journal of Artificial Intelligence Research
Universal voting protocol tweaks to make manipulation hard
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Where are the really hard manipulation problems? the phase transition in manipulating the veto rule
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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The stable marriage problem is a well-known problem of matching men to women so that no man and woman who are not married to each other both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors, to hospitals to matching students to schools. A well-known algorithm to solve this problem is the Gale---Shapley algorithm, which runs in quadratic time in the number of men/women. It has been proven that stable marriage procedures can always be manipulated. Whilst the Gale---Shapley algorithm is computationally easy to manipulate, we prove that there exist stable marriage procedures which are NP-hard to manipulate. We also consider the relationship between voting theory and stable marriage procedures, showing that voting rules which are NP-hard to manipulate can be used to define stable marriage procedures which are themselves NP-hard to manipulate. Finally, we consider the issue that stable marriage procedures like Gale---Shapley favour one gender over the other, and we show how to use voting rules to make any stable marriage procedure gender neutral.