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Preference-based alignment is pivotal for training large reasoning models; however, standard methods like Direct Preference Optimization (DPO) typically treat all preference pairs uniformly, overlooking the evolving utility of training…
We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). For an instance $I$ of SMI there may be many stable matchings, providing significantly different outcomes for the sets of…
Project-based learning improves student engagement and learning outcomes, yet allocating students to appropriately challenging projects while forming cognitively diverse teams remains difficult at scale. Traditional allocation methods…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
Meta-learning is a popular framework for learning with limited data in which an algorithm is produced by training over multiple few-shot learning tasks. For classification problems, these tasks are typically constructed by sampling a small…
We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…
We study control problems in the context of matching under preferences: We examine how a central authority, called the controller, can manipulate an instance of the Stable Marriage or Stable Roommates problems in order to achieve certain…
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case…
Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…
The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications.…
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 present new integer linear programming (ILP) models for NP-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals / Residents problem…
The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient…
In bipartite matching problems, agents on two sides of a graph want to be paired according to their preferences. The stability of a matching depends on these preferences, which in uncertain environments also reflect agents' beliefs about…
Recently MV18 identified and initiated work on the new problem of understanding structural relationships between the lattices of solutions of two "nearby" instances of stable matching. They also gave an application of their work to finding…
The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their…
We consider the problem of computing popular matchings in a bipartite graph G = (R U H, E) where R and H denote a set of residents and a set of hospitals respectively. Each hospital h has a positive capacity denoting the number of residents…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
Using school choice as a motivating example, we introduce a stylized model of a many-to-one matching market where the clearinghouse aims to implement contingent priorities, i.e., priorities that depend on the current assignment, to…
We investigate the complexity of approximately counting stable roommate assignments in two models: (i) the $k$-attribute model, in which the preference lists are determined by dot products of "preference vectors" with "attribute vectors"…