Stable marriage and indifference

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...

The structure of stable marriage with indifference

We consider the stable marriage problem where participants are permitted to express indifference in their preference lists (i.e., each list can be partially ordered). We prove that, in an instance where indifference takes the form of ties, the set of strongly stable matchings forms a distributive lattice. However, we show that this lattice structure may be absent if indifference is in the form ...

On Treewidth and Stable Marriage

Stable Marriage is a fundamental problem to both computer science and economics. Four well-known NP-hard optimization versions of this problem are the Sex-Equal Stable Marriage (SESM), Balanced Stable Marriage (BSM), max-Stable Marriage with Ties (max-SMT) and min-Stable Marriage with Ties (min-SMT) problems. In this paper, we analyze these problems from the viewpoint of Parameterized Complexit...

The Stable Marriage Problem

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...