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We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…
To understand the empirical success of approximate MAP inference, recent work (Lang et al., 2018) has shown that some popular approximation algorithms perform very well when the input instance is stable. The simplest stability condition…
We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…
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 this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features.…
In this paper, we consider the Hospital Residents problem (HR) and the Hospital Residents problem with Lower Quotas (HRLQ). In this model with two sided preferences, stability is a well accepted notion of optimality. However, in the…
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…
We study the Student Project Allocation problem with lecturer preferences over Students (SPA-S), which involves the assignment of students to projects based on student preferences over projects, lecturer preferences over students, and…
The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the…
Instances generation is crucial for linear programming algorithms, which is necessary either to find the optimal pivot rules by training learning method or to evaluate and verify corresponding algorithms. This study proposes a general…
In the Stable Marriage problem. when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents…
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…
In this paper, we begin by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, which are a man and a woman who rank each other first. Inversely, we examine…
Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance…
Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content…
In several two-sided markets, including labor and dating, agents typically have limited information about their preferences prior to mutual interactions. This issue can result in matching frictions, as arising in the labor market for…
We thoroughly study a generalized version of the classic Stable Marriage and Stable Roommates problems where agents may share partners. We consider two prominent stability concepts: ordinal stability [Aharoni and Fleiner, Journal of…
We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…
The classical stable marriage problem asks for a matching between a set of men and a set of women with no blocking pairs, which are pairs formed by a man and a woman who would both prefer switching from their current status to be paired up…