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On the Set of Stable Matchings in a Bipartite Graph
AbstractThe topic of stable matchings (marriages) in bipartite graphs gained popularity beginning from the appearance of the classical Gale and...
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Review of the Theory of Stable Matchings and Contract Systems
AbstractA review of works devoted to the theory of stable matchings or, more generally, of stable networks of contracts is given. A set (network) of...
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Affinely representable lattices, stable matchings, and choice functions
Birkhoff’s representation theorem (Birkhoff, Duke Math J 3(3):443–454, 1937) defines a bijection between elements of a distributive lattice and the...
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Critical Relaxed Stable Matchings with Two-Sided Ties
We consider the stable marriage problem in the presence of ties in preferences and critical vertices. The input to our problem is a bipartite graph...
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Matchings
Imagine that one is tasked with assigning hotel rooms, which are all for two occupants, to n guests, but where there is a list of couples who are...
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Computational Complexity of k-Stable Matchings
We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models....
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Perfect Matchings
Perfect matchings in graphs have been of interest ever since Tait showed that the four colour conjecture was equivalent to the statement that every...
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Diverse Pairs of Matchings
We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k , ask whether G has two...
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Algorithms and Complexity of Strongly Stable Non-crossing Matchings
A matching is called stable if it has no blocking pair, where a blocking pair is a man-woman pair, say (m, w), such that m and w are not matched with...
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On the Existence of Three-Dimensional Stable Matchings with Cyclic Preferences
We study the three-dimensional stable matching problem with cyclic preferences. This model involves three types of agents, with an equal number of...
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A short survey on stable polynomials, orientations and matchings
This is a short survey about the theory of stable polynomials and its applications. It gives self-contained proofs of two theorems of Schrijver. One...
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Finding Maximum Weakly Stable Matchings for Hospitals/Residents with Ties Problem via Heuristic Search
The Hospitals/Residents with Ties Problem is a many-one stable matching problem, in which residents need to be assigned to hospitals to meet their...
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Strongly Stable and Maximum Weakly Stable Noncrossing Matchings
In IWOCA 2019, Ruangwises and Itoh introduced stable noncrossing matchings , where participants of each side are aligned on each of two parallel...
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Proportional representation in matching markets: selecting multiple matchings under dichotomous preferences
Given a set of agents with approval preferences over each other, we study the task of finding k matchings fairly representing everyone’s preferences....
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Characterization of Super-Stable Matchings
An instance of the super-stable matching problem with incomplete lists and ties is an undirected bipartite graph...
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Disjoint Stable Matchings in Linear Time
We show that given a Stable Matching instance \(G\) as input, we...
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Two-Stage Stochastic Stable Matching
We introduce and study a two-stage stochastic stable matching problem between students and schools. A decision maker chooses a stable matching in a...
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