Related papers: Minimal instances with no weakly stable matching f…
We consider a learning problem for the stable marriage model under unknown preferences for the left side of the market. We focus on the centralized case, where at each time step, an online platform matches the agents, and obtains a noisy…
This paper develops a method to use singles' data in a non-parametric revealed preference setting of collective household choice. We use it to test the controversial assumption of preference stability between singles and couples, without…
The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
The efficient computation of large matchings with desirable guarantees is a crucial objective in market design. However, even in simple two-sided matching markets with weak ordinal preferences, finding a maximum-size stable matching is…
While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this…
We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences…
Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair…
Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…
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 Balanced Stable Marriage problem is a central optimization version of the classic Stable Marriage problem. Here, the output cannot be an arbitrary stable matching, but one that balances between the dissatisfaction of the two parties,…
We consider two-sided matching markets, and study the incentives of agents to circumvent a centralized clearing house by signing binding contracts with one another. It is well-known that if the clearing house implements a stable match and…
We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to…
The stable marriage problem requires one to find a marriage with no blocking pair. Given a matching that is not stable, Roth and Vande Vate have shown that there exists a sequence of matchings that leads to a stable matching in which each…
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…
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…
The Gale-Shapley algorithm for the Stable Marriage Problem is known to take $\Theta(n^2)$ steps to find a stable marriage in the worst case, but only $\Theta(n \log n)$ steps in the average case (with $n$ women and $n$ men). In 1976, Knuth…
Consider the stable matching problem on two sets. We introduce the concept of a preference cycle and show how its natural presence in stable matchings proves a series of classical results in an elementary way.
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
The research paper emphasizes that the Stable Matching problems are the same as the problems of stable configurations of Multi-stage Interconnection Networks (MIN). We have discusses the Stability Problems of Existing Regular Omega…