Lower bounds for the stable marriage problem and its variants
SIAM Journal on Computing
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Hard variants of stable marriage
Theoretical Computer Science
Stable Marriage with Incomplete Lists and Ties
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Improved approximation results for the stable marriage problem
ACM Transactions on Algorithms (TALG)
A 1.875: approximation algorithm for the stable marriage problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A Survey of the Stable Marriage Problem and Its Variants
ICKS '08 Proceedings of the International Conference on Informatics Education and Research for Knowledge-Circulating Society (icks 2008)
Better and Simpler Approximation Algorithms for the Stable Marriage Problem
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A (2 - c1/√N)-approximation algorithm for the stable marriage problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Elicitation and approximately stable matching with partial preferences
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We study the stable marriage problem in a distributed environment, in which there are 2n players, n men and n women, each holding a private ranking of the n persons of the opposite set, and there is a server who communicates with the players and finds a matching for them. We restrict our attention on two communication models: the sketch model and the query model. In the sketch model, each player compresses his/her ranking into a sketch and sends it to the server, while in the query model, the server itself adaptively queries individual bits on each player's ranking. We show that for the server to output even a slightly stable matching, in which a small constant fraction of matched pairs are stable, it must receive Ω(n2logn) bits from the players in the sketch model, and it must query Ω(n2logn) bits on their rankings in the query model. This implies that even to find a slightly stable matching, it is impossible to have an algorithm which compresses the input into a sketch of sub-linear size or to have an algorithm which runs in sub-linear time.