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In this paper, we consider one-to-one matchings between two disjoint groups of agents. Each agent has a preference over a subset of the agents in the other group, and these preferences may contain ties. Strong stability is one of the…

Computer Science and Game Theory · Computer Science 2024-01-08 Naoyuki Kamiyama

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…

Artificial Intelligence · Computer Science 2010-07-06 Mirco Gelain , Maria Silvia Pini , Francesca RossI , Kristen Brent Venable , Toby Walsh

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…

Computer Science and Game Theory · Computer Science 2020-05-19 Sushmita Gupta , Pallavi Jain , Sanjukta Roy , Saket Saurabh , Meirav Zehavi

We study many-to-one matching problems between institutions and individuals, where each institution may be matched to multiple individuals. The matching market includes couples, who view pairs of institutions as complementary. Institutions'…

Theoretical Economics · Economics 2025-07-11 Shashwat Khare , Souvik Roy

We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…

Computer Science and Game Theory · Computer Science 2026-01-14 Rohith Reddy Gangam , Tung Mai , Nitya Raju , Vijay V. Vazirani

Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the…

Computer Science and Game Theory · Computer Science 2021-05-20 Ágnes Cseh , Jannik Peters

In a stable matching problem there are two groups of agents, with agents on one side having their individual preferences for agents on another side as a potential match. It is assumed silently that agents can freely and costlessly ``switch"…

Combinatorics · Mathematics 2025-07-22 Boris Pittel , Kirill Rudov

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

The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…

Computer Science and Game Theory · Computer Science 2022-04-29 Kristóf Bérczi , Gergely Csáji , Tamás Király

In IWOCA 2019, Ruangwises and Itoh introduced stable noncrossing matchings, where participants of each side are aligned on each of two parallel lines, and no two matching edges are allowed to cross each other. They defined two stability…

Data Structures and Algorithms · Computer Science 2020-06-29 Koki Hamada , Shuichi Miyazaki , Kazuya Okamoto

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from…

Artificial Intelligence · Computer Science 2016-11-25 Maria Silvia Pini , Francesca Rossi , Brent Venable , Toby Walsh

Stable matching in a community consisting of men and women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley, who…

Data Structures and Algorithms · Computer Science 2021-12-14 Hugo Gimbert , Claire Mathieu , Simon Mauras

We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…

Data Structures and Algorithms · Computer Science 2024-07-16 Evripidis Bampis , Konstantinos Dogeas , Thomas Erlebach , Nicole Megow , Jens Schlöter , Amitabh Trehan

We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier and investigate other implications. We give…

Data Structures and Algorithms · Computer Science 2016-12-21 Marvin Künnemann , Daniel Moeller , Ramamohan Paturi , Stefan Schneider

The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…

Physics and Society · Physics 2018-06-26 Gui-Yuan Shi , Yi-Xiu Kong , Bo-Lun Chen , Guang-Hui Yuan , Rui-Jie Wu

We give a 3/2-approximation algorithm for stable matchings that runs in $O(m)$ time. The previously best known algorithm by McDermid has the same approximation ratio but runs in $O(n^{3/2}m)$ time, where $n$ denotes the number of people and…

Data Structures and Algorithms · Computer Science 2014-04-07 Katarzyna Paluch

We study stable matching problems with locality of information and control. In our model, each agent is a node in a fixed network and strives to be matched to another agent. An agent has a complete preference list over all other agents it…

Data Structures and Algorithms · Computer Science 2016-11-22 Martin Hoefer , Lisa Wagner

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

We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley[GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…

Discrete Mathematics · Computer Science 2025-12-23 Rohith Reddy Gangam , Tung Mai , Nitya Raju , Vijay V. Vazirani

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…

Computer Science and Game Theory · Computer Science 2018-10-09 Vijay Menon , Kate Larson