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Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…

Computer Science and Game Theory · Computer Science 2012-07-17 Haris Aziz

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 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

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

In two-sided matching markets, the agents are partitioned into two sets. 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 there are no blocking…

Computer Science and Game Theory · Computer Science 2013-02-26 Georgios Askalidis , Nicole Immorlica , Emmanouil Pountourakis

Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…

Computer Science and Game Theory · Computer Science 2018-12-14 Kitty Meeks , Baharak Rastegari

The stable matching problem sets the economic foundation of several practical applications ranging from school choice and medical residency to ridesharing and refugee placement. It is concerned with finding a matching between two disjoint…

Computer Science and Game Theory · Computer Science 2022-02-01 Angelina Brilliantova , Hadi Hosseini

In the marriage problem, a variant of the bi-parted matching problem, each member has a `wish-list' expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain…

Disordered Systems and Neural Networks · Physics 2015-06-25 Th. M. Nieuwenhuizen

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

Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…

Computer Science and Game Theory · Computer Science 2020-03-05 Daniel Lehmann

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

The popular matching problem is of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in the order of preference, possibly with ties. A matching M is popular if…

Data Structures and Algorithms · Computer Science 2019-12-23 Changyong Hu , Vijay K. Garg

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

In bipartite matching problems, agents on two sides of a graph want to be paired according to their preferences. The stability of a matching depends on these preferences, which in uncertain environments also reflect agents' beliefs about…

Computer Science and Game Theory · Computer Science 2025-11-10 Jonathan Shaki , Jiarui Gan , Sarit Kraus

In the fundamental Stable Marriage and Stable Roommates problems, there are inherent trade-offs between the size and stability of solutions. While in the former problem, a stable matching always exists and can be found efficiently using the…

Computer Science and Game Theory · Computer Science 2026-01-27 Frederik Glitzner , 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

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 consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching…

Data Structures and Algorithms · Computer Science 2018-04-10 Telikepalli Kavitha

An input to the Popular Matching problem, in the roommates setting, consists of a graph $G$ and each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there…

Data Structures and Algorithms · Computer Science 2018-03-28 Sushmita Gupta , Pranabendu Misra , Saket Saurabh , Meirav Zehavi

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