Related papers: Optimal Capacity Modification for Many-To-One Matc…
We consider many-to-one matching problems, where one side corresponds to applicants who have preferences and the other side to houses who do not have preferences. We consider two different types of this market: one, where the applicants…
The many-to-one stable matching problem provides the fundamental abstraction of several real-world matching markets such as school choice and hospital-resident allocation. The agents on both sides are often referred to as residents and…
In a multiple partners matching problem the agents can have multiple partners up to their capacities. In this paper we consider both the two-sided many-to-many stable matching problem and the one-sided stable fixtures problem under…
Motivated by the shortage of seats that the Chilean school choice system is facing, we introduce the problem of jointly increasing school capacities and finding a student-optimal assignment in the expanded market. Due to the theoretical and…
We consider the Hospitals/Residents (HR) problem in the presence of ties in hospital preferences. Among the three notions of stability, namely weak stability, strong stability, and super-stability, we focus on the notion of strong…
We study the problem of capacity modification in the many-to-one stable matching of workers and firms. Our goal is to systematically study how the set of stable matchings changes when some seats are added to or removed from the firms. We…
Given two point sets S and T, in a many-to-many matching between S and T each point in S is assigned to one or more points in T and vice versa. A generalization of the many-to-many matching problem is the limited capacity many-to-many…
The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. Previously considered criteria for evaluating proposed mechanisms…
We evaluate the goal of maximizing the number of individuals matched to acceptable outcomes. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize…
Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where…
Team assembly is a problem that demands trade-offs between multiple fairness criteria and computational optimization. We focus on four criteria: (i) fair distribution of workloads within the team, (ii) fair distribution of skills and…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…
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…
I settle the computational complexity of student-project-resource matching-allocation problems, in which students and resources are assigned to projects \citep{pc2017}. A project's capacity for students is endogenously determined by the…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
We consider the problem of allocating applicants to courses, where each applicant has a subset of acceptable courses that she ranks in strict order of preference. Each applicant and course has a capacity, indicating the maximum number of…
Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to…
In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…
In the house allocation problem with lower and upper quotas, we are given a set of applicants and a set of projects. Each applicant has a strictly ordered preference list over the projects, while the projects are equipped with a lower and…
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…