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In the Stable Roommates problem, we seek a stable matching of the agents into pairs, in which no two agents have an incentive to deviate from their assignment. It is well known that a stable matching is unlikely to exist, but a stable…

Data Structures and Algorithms · Computer Science 2024-11-26 Frederik Glitzner , David Manlove

In the well-studied Stable Roommates problem, we seek a stable matching of agents into pairs, where no two agents prefer each other over their assigned partners. However, some instances of this problem are unsolvable, lacking any stable…

Computer Science and Game Theory · Computer Science 2025-07-08 Frederik Glitzner , David Manlove

We study (coalitional) exchange stability, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a…

Computer Science and Game Theory · Computer Science 2021-05-18 Jiehua Chen , Adrian Chmurovic , Fabian Jogl , Manuel Sorge

We consider the problem of stable matching with dynamic preference lists. At each time step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an…

Computer Science and Game Theory · Computer Science 2016-06-29 Varun Kanade , Nikos Leonardos , Frédéric Magniez

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 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

The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…

Disordered Systems and Neural Networks · Physics 2007-05-23 Stephan Mertens

The stable roommates problem with $n$ agents has worst case complexity $O(n^2)$ in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity…

Data Structures and Algorithms · Computer Science 2015-01-22 Stephan Mertens

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI,…

Discrete Mathematics · Computer Science 2017-09-01 Ágnes Cseh , Robert W. Irving , David F. Manlove

In their seminal work on the Stable Marriage Problem (SM), Gale and Shapley introduced a generalization of SM referred to as the Stable Roommates Problem (SR). An instance of SR consists of a set of $2n$ agents, and each agent has…

Computational Complexity · Computer Science 2025-02-12 Will Rosenbaum

The stable roommates problem is a non-bipartite version of the stable matching problem in a bipartite graph. In this paper, we consider the stable roommates problem with ties. In particular, we focus on strong stability, which is one of the…

Computer Science and Game Theory · Computer Science 2025-10-21 Naoyuki Kamiyama

In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if…

Computer Science and Game Theory · Computer Science 2013-05-14 Georgios Askalidis , Nicole Immorlica , Augustine Kwanashie , David F. Manlove , Emmanouil Pountourakis

Since the early days of research in algorithms and complexity, the computation of stable matchings is a core topic. While in the classic setting the goal is to match up two agents (either from different "gender" (this is Stable Marriage) or…

Computational Complexity · Computer Science 2021-04-02 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for…

Computer Science and Game Theory · Computer Science 2019-11-25 Robert Bredereck , Jiehua Chen , Dušan Knop , Junjie Luo , Rolf Niedermeier

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Specifically, given a stable matching $M_1$, a set $Q$ of forced pairs, and a set $P$ of forbidden pairs, we want to find a stable matching that includes…

Computer Science and Game Theory · Computer Science 2022-11-23 Niclas Boehmer , Klaus Heeger

A recently introduced restricted variant of the multidimensional stable roommate problem is the roommate diversity problem: each agent belongs to one of two types (e.g., red and blue), and the agents' preferences over the coalitions solely…

Computer Science and Game Theory · Computer Science 2023-01-06 Steven Ge , Toshiya Itoh

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

We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…

Computer Science and Game Theory · Computer Science 2022-05-17 Matthias Bentert , Niclas Boehmer , Klaus Heeger , Tomohiro Koana

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

This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance…

Computational Complexity · Computer Science 2023-05-23 Kazuo Iwama , Shuichi Miyazaki