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Related papers: Sequences of the Stable Matching Problem

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Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. In…

Combinatorics · Mathematics 2026-01-13 Byron Chin , Marcus Michelen

In the Stable Roommates Problem (SR), a set of $2n$ agents rank one another in a linear order. The goal is to find a matching that is stable: one that has no pair of agents who mutually prefer each other over their assigned partners. We…

Data Structures and Algorithms · Computer Science 2026-05-11 Christine T. Cheng , Will Rosenbaum

Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…

Combinatorics · Mathematics 2017-07-25 Boris Pittel

We consider a variant of socially stable marriage problem where preference lists may be incomplete, may contain ties and may have bounded length. In real world application like NRMP and Scottish medical matching scheme such restrictions…

Data Structures and Algorithms · Computer Science 2016-07-25 Ashish Shrivastava , C. Pandu Rangan

The stable marriage problem requires one to find a marriage with no blocking pair. Given a matching that is not stable, Roth and Vande Vate have shown that there exists a sequence of matchings that leads to a stable matching in which each…

Computer Science and Game Theory · Computer Science 2023-05-18 Vijay Kumar Garg , Changyong Hu

The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint…

Computational Complexity · Computer Science 2018-02-21 Jiehua Chen , Danny Hermelin , Manuel Sorge , Harel Yedidsion

The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications.…

Artificial Intelligence · Computer Science 2013-05-03 Sofie De Clercq , Steven Schockaert , Martine De Cock , Ann Nowé

The stable marriage (SM) 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. In the classical formulation, n…

Artificial Intelligence · Computer Science 2010-07-07 M. Gelain , M. S. Pini , F. Rossi , K. B. Venable , T. Walsh

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…

Computer Science and Game Theory · Computer Science 2014-07-28 Linda Farczadi , Konstantinos Georgiou , Jochen Könemann

The Stable Roommates problems are characterized by the preferences of agents over other agents as roommates. A solution is a partition of the agents into pairs that are acceptable to each other (i.e., they are in the preference lists of…

Artificial Intelligence · Computer Science 2025-07-29 Müge Fidan , Esra Erdem

In the stable marriage and roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually accepted agents. If any…

Discrete Mathematics · Computer Science 2016-06-01 Ágnes Cseh , David F. Manlove

Suppose each of $n$ men and $n$ women is located at a point in a metric space. A woman ranks the men in order of their distance to her from closest to farthest, breaking ties at random. The men rank the women similarly. An interesting…

Computer Science and Game Theory · Computer Science 2017-10-17 Hossein Karkeh Abadi , Balaji Prabhakar

The stable roommates problem can admit multiple different stable matchings. We have different criteria for deciding which one is optimal, but computing those is often NP-hard. We show that the problem of finding generous or rank-maximal…

Data Structures and Algorithms · Computer Science 2021-10-07 Sofia Simola , David Manlove

The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…

Computer Science and Game Theory · Computer Science 2021-07-12 Michael McKay , David Manlove

Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…

Combinatorics · Mathematics 2024-06-18 Boris Pittel

The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their…

Computer Science and Game Theory · Computer Science 2020-04-21 Robert Bredereck , Jiehua Chen , Ugo Paavo Finnendahl , Rolf Niedermeier

Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new…

Artificial Intelligence · Computer Science 2020-02-19 Sofie De Clercq , Steven Schockaert , Martine De Cock , Ann Nowé

We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences…

Data Structures and Algorithms · Computer Science 2009-10-25 Chien-Chung Huang

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…

Computational Complexity · Computer Science 2014-10-10 Rafail Ostrovsky , Will Rosenbaum

The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that…

Artificial Intelligence · Computer Science 2020-08-10 Esra Erdem , Muge Fidan , David Manlove , Patrick Prosser