A stable marriage requires communication

A Stable Marriage Requires Communication

The Gale-Shapely algorithm for the Stable Marriage Problem is known to take Θ(n2) steps to find a stable marriage in the worst case, but only Θ(n log n) steps in the average case (with n women and n men). In 1976, Knuth asked whether the worst-case running time can be improved in a model of computation that does not require sequential access to the whole input. A partial negative answer was giv...

On The Communication Complexity of Finding an (Approximate) Stable Marriage

In this paper, we consider the communication complexity of protocols that compute stable matchings. We work within the context of Gale and Shapley’s original stable marriage problem[3]: n men and n women each privately hold a total and strict ordering on all of the members of the opposite gender. They wish to collaborate in order to find a stable matching—a pairing of the men and women such tha...

The Stable Marriage Problem

Stable Marriage and Indifference

It is well known that every instance of the classical stable marriage problem admits at least one stable matching, and that such a matching can be found in O(n’) time by application of the Gale/Shapley algorithm. In the classical version of the problem, each person must rank the members of the opposite sex in strict order of preference. In practical applications, a person may not wish (or be ab...

Distributed Stable Marriage Problem

The Stable Marriage Problem is a combinatorial problem which can be solved by a centralized algorithm in polynomial time. This requires to make public lists of preferences which agents would like to keep private. With this aim, we define the distributed version of this problem, and we provide a constraint-based approach that solves it keeping privacy. We give empirical results on the proposed a...