Related papers: Stable marriage and roommates problems with restri…
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
We study parameterized approximability of three optimization problems related to stable matching: (1) Min-BP-SMI: Given a stable marriage instance and a number k, find a size-at-least-k matching that minimizes the number $\beta$ of blocking…
In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…
In many economic contexts, agents from a same population team up to better exploit their human capital. In such contexts (often called "roommate matching problems"), stable matchings may fail to exist even when utility is transferable. We…
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…
We introduce a new and broader formulation of the stable marriage problem (SMP), called the stable polygamy problem (SPP), where multiple individuals from a larger group $L$ of $|L|$ individuals can be matched with a single individual from…
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley[GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly…
Consider the standard hospitals/residents problem, or the two-sided many-to-one stable matching problem, and assume that the true preference lists of both sides are complete and strict. The lists actually submitted, however, are truncated.…
The Stable Matching Problem with Couples (SMP-C) is a ubiquitous real-world extension of the stable matching problem (SMP) involving complementarities. Although SMP can be solved in polynomial time, SMP-C is NP-Complete. Hence, it is not…
Stable matching in a community consisting of men and women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley, who…
The stable marriage problem and its extensions have been extensively studied, with much of the work in the literature assuming that agents fully know their own preferences over alternatives. This assumption however is not always practical…
We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each…
We study popularity for matchings under preferences. This solution concept captures matchings that do not lose against any other matching in a majority vote by the agents. A popular matching is said to be robust if it is popular among…
Robust Stable Marriage (RSM) is a variant of the classical Stable Marriage problem, where the robustness of a given stable matching is measured by the number of modifications required for repairing it in case an unforeseen event occurs. We…
We present a polynomial-time $\frac{3}{2}$-approximation algorithm for the problem of finding a maximum-cardinality stable matching in a many-to-many matching model with ties and laminar constraints on both sides. We formulate our problem…
The Stable Marriage problem (SM), solved by the famous deferred acceptance algorithm of Gale and Shapley (GS), has many natural generalizations. If we allow ties in preferences, then the problem of finding a maximum stable matching becomes…
We are given a bipartite graph $G = \left( A \cup B, E \right)$. In the one-sided model, every $a \in A$ (often called agents) ranks its neighbours $z \in N_{a}$ strictly, and no $b \in B$ has any preference order over its neighbours $y \in…
The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in a complete graph, there exists a linear inequality…