Scaling Behavior in the Stable Marriage Problem

The Stable Marriage Problem

The exchange-stable marriage problem

In this paper we consider instances of stable matching problems, namely the classical Stable Marriage (SM) and Stable Roommates (SR) problems and their variants. In such instances we consider a stability criterion that has recently been proposed, that of exchange-stability. In particular, we prove that ESM – the problem of deciding, given an SM instance, whether an exchange-stable matching exis...

The Unsplittable Stable Marriage Problem

The Gale-Shapley “propose/reject” algorithm is a wellknown procedure for solving the classical stable marriage problem. In this paper we study this algorithm in the context of the many-to-many stable marriage problem, also known as the stable allocation or ordinal transportation problem. We present an integral variant of the GaleShapley algorithm that provides a direct analog, in the context of...

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...

Popular Matchings in the Stable Marriage Problem

The input is a bipartite graph G = (A ∪B ,E) where each vertex u ∈ A ∪B ranks its neighbors in a strict order of preference. This is the same as an instance of the stable marriage problem with incomplete lists. A matching M∗ is said to be popular if there is no matching M such that more vertices are better off in M than in M∗. Any stable matching of G is popular, however such a matching is a mi...