Related papers: Understanding popular matchings via stable matchin…
We study the many-to-many bipartite matching problem in the presence of preferences where ties, as well as lower quotas, may appear on both sides of the bipartition. The input is a bipartite graph $G=(A \cup B, E)$, where each vertex in $A…
A probabilistic approach to the stable matching problem has been identified as an important research area with several important open problems. When considering random matchings, ex-post stability is a fundamental stability concept. A…
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…
We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
Let $G$ be a graph and suppose we are given, for each $v \in V(G)$, a strict ordering of the neighbors of $v$. A set of matchings ${\cal M}$ of $G$ is called internally stable if there are no matchings $M,M' \in {\cal M}$ such that an edge…
An instance $I$ of the Stable Matching Problem (SMP) is given by a bipartite graph with a preference list of neighbors for every vertex. A swap in $I$ is the exchange of two consecutive vertices in a preference list. A swap can be viewed as…
We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions'…
It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a…
Given a set $A$ of $n$ people and a set $B$ of $m \geq n$ items, with each person having a list that ranks his/her preferred items in order of preference, we want to match every person with a unique item. A matching $M$ is called popular if…
The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…
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…
Let $G$ be a digraph where every node has preferences over its incoming edges. The preferences of a node extend naturally to preferences over branchings, i.e., directed forests; a branching $B$ is popular if $B$ does not lose a head-to-head…
Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…
We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…
We study ex-post fairness in the object allocation problem where objects are valuable and commonly owned. A matching is fair from individual perspective if it has only inevitable envy towards agents who received most preferred objects --…
In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…
We study the Reaching Stable Marriage via Divorces (DivorceSM) problem of deciding, given a Stable Marriage instance and an initial matching $M$ , whether there exists a stable matching which is reachable from $M$ by divorce operations as…