# A Survey of the Stable Marriage Problem and Its Variants

@article{Iwama2008ASO, title={A Survey of the Stable Marriage Problem and Its Variants}, author={Kazuo Iwama and Shuichi Miyazaki}, journal={International Conference on Informatics Education and Research for Knowledge-Circulating Society (icks 2008)}, year={2008}, pages={131-136} }

The stable marriage problem is to find a matching between men and women, considering preference lists in which each person expresses his/her preference over the members of the opposite gender. The output matching must be stable, which intuitively means that there is no man- woman pair both of which have incentive to elope. This problem was introduced in 1962 in the seminal paper of Gale and Shapley, and has attracted researchers in several areas, including mathematics, economics, game theory…

## 146 Citations

### An Introduction to Optimal Stable Marriage Problems and Argumentation Frameworks

- EconomicsAI³@AI*IA
- 2019

Weighted Abstract Argumentation is used to represent optimality criteria in Optimal SM problems, where some matchings are better than others: criteria may consider only the preference of either men, or women, or a more balanced view obtained by differently combining the preferences of both of them.

### Improved Paths to Stability for the Stable Marriage Problem

- MathematicsArXiv
- 2020

This paper presents an algorithm that achieves stability in a sequence of matchings of length $O(n^2)$ and gives an efficient algorithm to find the stable matching closest to the given initial matching under an appropriate distance function between matchings.

### Finding “optimal” stable marriages with ties via local search

- Computer Science2016 Eighth International Conference on Knowledge and Systems Engineering (KSE)
- 2016

A local search based algorithm which attempts to find egalitarian and sex-equal stable matchings in the stable marriage problem with ties, based on the dominance of stable matching with respect to men.

### Finding MAX-SMTI for Stable Marriage with Ties and Bounded Preference Lists

- Computer Science2019 International Conference on Advanced Computing and Applications (ACOMP)
- 2019

A constraint satisfaction based algorithm to find a maximum cardinality weakly stable matching for a given instance of the classical stable marriage problem is presented and a comparison against a well-known algorithm in the field is offered.

### An Optimal Algorithm for Stable Marriage Problem

- Computer Science
- 2018

This paper suggests always get the optimal stable matching on all occasions in order to overcome the shortcomings of MP and WP.

### Farsighted Collusion in Stable Marriage Problem

- EconomicsArXiv
- 2019

It is argued that the unique optimal collusion matching which is farsightedly stable is actually stronger than a Strong Nash Equilibrium - no alternative feasible coalition exists which can offer at least one member a strictly better outcome under these assumptions.

### Linear Time Local Approximation Algorithm for Maximum Stable Marriage

- Computer ScienceAlgorithms
- 2013

A two-sided market under incomplete preference lists with ties, where the goal is to find a maximum size stable matching, is considered, and a very natural, economically reasonable, local, linear time algorithm is presented.

### A New Perspective to Stable Marriage Problem in Profit Maximization of Matrimonial Websites

- Computer ScienceJ. Inf. Process. Syst.
- 2018

This paper has proposed an enhancement to the SMP by computing a weighted score for the users registered at matrimonial websites and shown that the proposed genetic algorithm based approaches outperform the existing Gale-Shapley algorithm on the dataset crawled from matrimony websites.

### Matching-Updating Mechanism: A Solution for the Stable Marriage Problem with Dynamic Preferences

- EconomicsEntropy
- 2022

We studied the stable marriage problem with dynamic preferences. The dynamic preference model allows the agent to change its preferences at any time, which may cause instability in a matching.…

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