Related papers: Strongly Stable and Maximum Weakly Stable Noncross…
In this paper, we consider the communication complexity of protocols that compute stable matchings. We work within the context of Gale and Shapley's original stable marriage problem\cite{GS62}: $n$ men and $n$ women each privately hold a…
Given an indeterminate string pattern $p$ and an indeterminate string text $t$, the problem of order-preserving pattern matching with character uncertainties ($\mu$OPPM) is to find all substrings of $t$ that satisfy one of the possible…
Since the early days of research in algorithms and complexity, the computation of stable matchings is a core topic. While in the classic setting the goal is to match up two agents (either from different "gender" (this is Stable Marriage) or…
Matching algorithms have demonstrated great success in several practical applications, but they often require centralized coordination and plentiful information. In many modern online marketplaces, agents must independently seek out and…
This paper introduces a unified framework for stable matching, which nests the traditional definition of stable matching in finite markets and the continuum definition of stable matching from Azevedo and Leshno (2016) as special cases.…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
Many countries around the world, including Korea, use the school choice lottery system. However, this method has a problem in that many students are assigned to less-preferred schools based on the lottery results. In addition, the task of…
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…
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…
The stable marriage problem and its extensions have been extensively studied, with much of the work in the literature assuming that agents fully know their own preferences over alternatives. This assumption however is not always practical…
In the roommate matching model, given a set of 2n agents and n rooms, we find an assignment of a pair of agents to a room. Although the roommate matching problem is well studied, the study of the model when agents have preference over both…
The Hospital Residents problem with sizes (HRS) is a generalization of the well-studied hospital residents (HR) problem. In the HRS problem, an agent $a$ has a size $s(a)$ and the agent occupies $s(a)$ many positions of the hospital $h$…
While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this…
The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic…
This paper studies matching markets where institutions are matched with possibly more than one individual. The matching market contains some couples who view the pair of jobs as complements. First, we show by means of an example that a…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the…
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…
We consider a far generalization of the well-known stable roommates and non-bipartite stable allocation problems. In its setting, one is given a finite non-bipartite graph $G=(V,E)$ with nonnegative integer edge capacities $b(e)\in{\mathbb…
We consider a model of stable edge sets (``matchings'') in a bipartite graph $G=(V,E)$ in which the preferences for vertices of one side (``firms'') are given via choice functions subject to standard axioms of consistency, substitutability…