Related papers: Stable Marriage with Multi-Modal Preferences
The topic of stable matchings (marriages) in a bipartite graph has become widely popular, starting with the appearance of the classical work by Gale and Shapley. We give a detailed survey on selected known results in this field that…
Roommate problems with convex preferences always have stable matchings. Efficiency and individual rationality are, moreover, compatible with strategyproofness in such convex roommate problems. Both of these results fail without the…
In this paper, we construct and compare algorithmic approaches to solve the Preference Consistency Problem for preference statements based on hierarchical models. Instances of this problem contain a set of preference statements that are…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
A stable joint plan should guarantee the achievement of a designer's goal in a multi-agent environment, while ensuring that deviations from the prescribed plan would be detected. We present a computational framework where stable joint plans…
We present an n-ary constraint for the stable marriage problem. This constraint acts between two sets of integer variables where the domains of those variables represent preferences. Our constraint enforces stability and disallows bigamy.…
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…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension in the ambient space of the data manifolds of interest, and…
Stable matchings have been studied extensively in social choice literature. The focus has been mostly on integral matchings, in which the nodes on the two sides are wholly matched. A fractional matching, which is a convex combination of…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
We generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph $G=(N,E)$, with an integer vertex capacity function $b$ and an edge weighting $w$. The set $N$ consists of a number of…
In the theory of two-sided matching markets there are two well-known models: the marriage model (where no money is involved) and the assignment model (where payments are involved). Roth and Sotomayor (1990) asked for an explanation for the…
Many allocation problems in multiagent systems rely on agents specifying cardinal preferences. However, allocation mechanisms can be sensitive to small perturbations in cardinal preferences, thus causing agents who make ``small" or…
We consider the situation in which an organizer is trying to convene an event, and needs to choose a subset of agents to be invited. Agents have preferences over how many attendees should be at the event and possibly also who the attendees…
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…
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…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
The Stable Matching Problem with Couples (SMP-C) is a ubiquitous real-world extension of the stable matching problem (SMP) involving complementarities. Although SMP can be solved in polynomial time, SMP-C is NP-Complete. Hence, it is not…