Related papers: New algorithms for matching problems
In the Gale-Shapley model of two-sided matching, it is well known that for generic preferences, the outcomes for each side can vary dramatically in the male-optimal vs. female-optimal stable matchings. In this paper, we show that under a…
The stable marriage problem, as addressed by Gale and Shapely [1] consists of providing a bipartite matching between n " boys " and n " girls "-each of whom have a totally ordered preference list over the other set-such that there exists no…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
Real-life tools for decision-making in many critical domains are based on ranking results. With the increasing awareness of algorithmic fairness, recent works have presented measures for fairness in ranking. Many of those definitions…
The algorithmic fairness of predictive analytic tools in the public sector has increasingly become a topic of rigorous exploration. While instruments pertaining to criminal recidivism and academic admissions, for example, have garnered much…
The theory of two-sided matching has been extensively developed and applied to many real-life application domains. As the theory has been applied to increasingly diverse types of environments, researchers and practitioners have encountered…
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…
For most people, social contacts play an integral part in finding a new job. As observed by Granovetter's seminal study, the proportion of jobs obtained through social contacts is usually large compared to those obtained through postings or…
We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information. Our model is motivated by the…
Two-sided matching markets, environments in which two disjoint groups of agents seek to partner with one another, arise in several contexts. In static, centralized markets where agents know their preferences, standard algorithms can yield a…
We study the assignment problem of objects to agents with heterogeneous preferences under distributional constraints. Each agent is associated with a publicly known type and has a private ordinal ranking over objects. We are interested in…
In this work, we analyze the influence of a single strategic agent on the quality of the other agents' matchings in a matching market. We consider a stable matching problem with $n$ men and $n$ women when preferences are drawn uniformly…
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 setting of online algorithms, the input is initially not present but rather arrive one-by-one over time and after each input, the algorithm has to make a decision. Depending on the formulation of the problem, the algorithm might be…
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…
We study the problem of approximate social welfare maximization (without money) in one-sided matching problems when agents have unrestricted cardinal preferences over a finite set of items. Random priority is a very well-known…
We study the design of a decentralized two-sided matching market in which agents' search is guided by the platform. There are finitely many agent types, each with (potentially random) preferences drawn from known type-specific…
The online bipartite matching problem, extensively studied in the literature, deals with the allocation of online arriving vertices (items) to a predetermined set of offline vertices (agents). However, little attention has been given to the…
This paper studies a matching problem in which a group of agents cooperate with agents on two sides. In environments with either nontransferable or transferable utilities, we demonstrate that a stable outcome exists when cooperations…
Our input is a bipartite graph $G = (A \cup B,E)$ where each vertex in $A \cup B$ has a preference list strictly ranking its neighbors. The vertices in $A$ and in $B$ are called students and courses, respectively. Each student $a$ seeks to…