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We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). In particular, we seek stable matchings that are optimal with respect to profile, which is a vector that indicates the…
We study the stable marriage problem in the partial information setting where the agents, although they have an underlying true strict linear order, are allowed to specify partial orders. Specifically, we focus on the case where the agents…
Statistical matching is an effective method for estimating causal effects in which treated units are paired with control units with ``similar'' values of confounding covariates prior to performing estimation. In this way, matching helps…
In stable matching, one must find a matching between two sets of agents, commonly men and women, or job applicants and job positions. Each agent has a preference ordering over who they want to be matched with. Moreover a matching is said to…
Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible…
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…
We consider stable and popular matching problems in arbitrary graphs, which are referred to as stable roommates instances. We extend the 3/2-approximation algorithm for the maximum size weakly stable matching problem to the roommates case,…
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…
We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…
We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…
This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete…
A recent line of research concerns the problem of soft happy colouring (SHC), which requires that a partially coloured graph be extended to a complete colouring to maximise local agreements, so that as many vertices as possible end up…
We consider popular matching problems in both bipartite and non-bipartite graphs with strict preference lists. It is known that every stable matching is a min-size popular matching. A subclass of max-size popular matchings called dominant…
The stable roommates problem is a non-bipartite version of the stable matching problem in a bipartite graph. In this paper, we consider the stable roommates problem with ties. In particular, we focus on strong stability, which is one of the…
We study the Stable Fixtures problem, a many-to-many generalisation of the classical non-bipartite Stable Roommates matching problem. Building on the foundational work of Tan on stable partitions, we extend his results to this significantly…
We study matching markets with ties, where workers on one side of the market may have tied preferences over jobs, determined by their matching utilities. Unlike classical two-sided markets with strict preferences, no single stable matching…
Earlier we introduced the notion of a stable set of points (SSP). We proved that a CNF formula is unsatisfiable iff there is a set of points (i.e. complete assignments) that is stable with respect to this formula. Experiments showed that…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
We study the problem of repeated two-sided matching with uncertain preferences (two-sided bandits), and no explicit communication between agents. Recent work has developed algorithms that converge to stable matchings when one side (the…
We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…