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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…
This chapter surveys the application of matching theory to school choice, motivated by the shift from neighborhood assignment systems to choice-based models. Since educational choice is not mediated by price, the design of allocation…
In the fundamental Stable Marriage and Stable Roommates problems, there are inherent trade-offs between the size and stability of solutions. While in the former problem, a stable matching always exists and can be found efficiently using the…
We investigate the following many-to-one stable matching problem with diversity constraints (SMTI-Diverse): Given a set of students and a set of colleges which have preferences over each other, where the students have overlapping types, and…
We study the course allocation problem, where universities assign course schedules to students. The current state-of-the-art mechanism, Course Match, has one major shortcoming: students make significant mistakes when reporting their…
Workforce Scheduling and Routing Problems (WSRP) are very common in many practical domains, and usually, have a number of objectives. Illumination algorithms such as Map-Elites (ME) have recently gained traction in application to {\em…
Transportation networks frequently employ hub-and-spoke network architectures to route flows between many origin and destination pairs. Hub facilities work as switching points for flows in large networks. In this study, we deal with a…
We introduce a constrained priority mechanism that combines outcome-based matching from machine-learning with preference-based allocation schemes common in market design. Using real-world data, we illustrate how our mechanism could be…
We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which…
Motivated by our collaboration with a major refugee resettlement agency in the U.S., we study a dynamic matching problem where each new arrival (a refugee case) must be matched immediately and irrevocably to one of the static resources (a…
The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…
Reciprocal recommender systems (RRSs) are crucial in online two-sided matching platforms, such as online job or dating markets, as they need to consider the preferences of both sides of the match. The concentration of recommendations to a…
In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures?…
We consider the well-studied Hospital Residents (HR) problem in the presence of lower quotas (LQ). The input instance consists of a bipartite graph $G = (\mathcal{R} \cup \mathcal{H}, E)$ where $\mathcal{R}$ and $\mathcal{H}$ denote sets of…
The dominating set reconfiguration problem is defined as determining, for a given dominating set problem and two among its feasible solutions, whether one is reachable from the other via a sequence of feasible solutions subject to a certain…
We examine a controlled school choice model where students are categorized into different types, and the distribution of these types within a school influences its priority structure. This study provides a general framework that integrates…
The Hospitals / Residents problem with Couples (HRC) is a generalisation of the classical Hospitals / Resident problem (HR) that is important in practical applications because it models the case where couples submit joint preference lists…
For a two-sided ($n$ men/$n$ women) stable matching problem) Gale and Shapley studied a proposal algorithm (men propose/women select, or the other way around), that determines a matching, not blocked by any unmatched pair. Irving used this…
When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may…
In many labor markets, workers and firms are connected via affiliative relationships. A management consulting firm wishes to both accept the best new workers but also place its current affiliated workers at strong firms. Similarly, a…