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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

We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…

Computer Science and Game Theory · Computer Science 2020-12-25 Ioannis Caragiannis , Aris Filos-Ratsikas , Panagiotis Kanellopoulos , Rohit Vaish

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

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

We initiate the study of distortion in stable matching. Concretely, we aim to design algorithms that have limited access to the agents' cardinal preferences and compute stable matchings of high quality with respect to some aggregate…

Computer Science and Game Theory · Computer Science 2026-02-17 Aris Filos-Ratsikas , Georgios Kalantzis

Let G = ((A,B),E) be an instance of the stable marriage problem where every vertex ranks its neighbors in a strict order of preference. A matching M in G is popular if M does not lose a head-to-head election against any matching. Popular…

Data Structures and Algorithms · Computer Science 2020-05-06 Yuri Faenza , Telikepalli Kavitha

In 1976, Knuth asked if the stable marriage problem (SMP) can be generalized to marriages consisting of 3 genders. In 1988, Alkan showed that the natural generalization of SMP to 3 genders ($3$GSM) need not admit a stable marriage. Three…

Computational Complexity · Computer Science 2014-12-04 Rafail Ostrovsky , Will Rosenbaum

When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may…

Computer Science and Game Theory · Computer Science 2022-11-09 Niclas Boehmer , Klaus Heeger , Rolf Niedermeier

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 introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…

Multiagent Systems · Computer Science 2018-01-10 Jiehua Chen , Rolf Niedermeier , Piotr Skowron

The Stable Marriage Problem, as proposed by Gale and Shapley, considers producing a bipartite matching between two equally sized sets of boys (proposers) and respectively girls (acceptors), each member having a total preference order over…

Computer Science and Game Theory · Computer Science 2019-05-28 Mircea Digulescu

We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…

Computer Science and Game Theory · Computer Science 2022-09-08 Naoyuki Kamiyama

We show that given a SM instance G as input we can find a largest collection of pairwise edge-disjoint stable matchings of G in time linear in the input size. This extends two classical results: 1. The Gale-Shapley algorithm, which can find…

Data Structures and Algorithms · Computer Science 2021-07-06 Aadityan Ganesh , Vishwa Prakash HV , Prajakta Nimbhorkar , Geevarghese Philip

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

Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching…

Data Structures and Algorithms · Computer Science 2026-04-21 Brian Brubach , Nathaniel Grammel , Will Ma , Calum MacRury , Aravind Srinivasan

We propose a model for recoverable robust optimization with commitment. Given a combinatorial optimization problem and uncertainty about elements that may fail, we ask for a robust solution that, after the failing elements are revealed, can…

Data Structures and Algorithms · Computer Science 2023-06-16 Felix Hommelsheim , Nicole Megow , Komal Muluk , Britta Peis

In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…

Computer Science and Game Theory · Computer Science 2025-02-11 Gergely Csáji

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

Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both…

Computer Science and Game Theory · Computer Science 2025-02-27 Felipe Garrido-Lucero , Rida Laraki

The goal in {\em reconfiguration problems} is to compute a {\em gradual transformation} between two feasible solutions of a problem such that all intermediate solutions are also feasible. In the {\em Matching Reconfiguration Problem} (MRP),…

Data Structures and Algorithms · Computer Science 2020-05-07 Noam Solomon , Shay Solomon