Hard variants of stable marriage

@article{Manlove2002HardVO,
  title={Hard variants of stable marriage},
  author={David Manlove and Robert W. Irving and Kazuo Iwama and S. Miyazaki and Yasufumi Morita},
  journal={Theor. Comput. Sci.},
  year={2002},
  volume={276},
  pages={261-279}
}
View via Publisher
doi.org
302 Citations
Highly Influential Citations
36
Background Citations
175
Methods Citations
29
Results Citations
3

302 Citations

A Survey of the Stable Marriage Problem and Its Variants
  • K. IwamaS. Miyazaki
  • Economics
    International Conference on Informatics Education and Research for Knowledge-Circulating Society (icks 2008)
  • 2008
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…
The stable matching problem and its generalizations: an algorithmic and game theoretical approach
We say that a market situation is stable in a general sense, if there is no set of agents such that all of them are interested in creating a new cooperation (after breaking their other eventual…
Local Search for Stable Marriage Problems with Ties and Incomplete Lists
TLDR
This work considers a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex, and studies the problem of finding a stable matching that marries as many people as possible.
Size Versus Stability in the Marriage Problem
TLDR
This work shows that the problem of finding a maximum cardinality matching in I that admits the smallest number of blocking pairs is NP-hard and not approximable within n, for any ε > 0, unless P=NP, where n is the number of men in I.
Stable Marriage with General Preferences
TLDR
It is proved that the problem of deciding whether a fixed 2D perfect matching can be extended to a 3D stable matching is NP-complete, showing this way that a natural attempt to resolve the existence (or not) of3D stable matchings is bound to fail.
On the approximability of the stable marriage problem with one-sided ties
TLDR
A refined analysis of an approximation algorithm given by Huang and Telikepalli (IPCO14) for the stable marriage problem with one-sided ties is given, which shows an improved 13/9 -approximation factor for the problem.
A Study Of Stable Marriage Problems With Ties
  • S. Scott
  • Mathematics, Computer Science
  • 2005
TLDR
The concept of a rotation is extended, essentially the minimum difference between stable matchings, to super-stability, and it is shown that a directed acyclic graph can be constructed to represent precedence amongst these meta-rotations.
Stable marriage and roommate problems with individual-based stability
TLDR
The computational complexity of checking the existence and computing individual-based stable matchings for the marriage and roommate settings is characterized and some of the key computational results carry over to different classes of hedonic games and network formation games for which individual- based stability has already been of much interest.
Randomized Approximation of the Stable Marriage Problem
Local Search Approaches in Stable Matching Problems
TLDR
This work considers both the classical stable marriage problem and one of its useful variations (denoted SMTI (Stable Marriage with Ties and Incomplete lists)) where the men and women express their preferences in the form of an incomplete preference list with ties over a subset of the members of the other sex.
...
...

References

SHOWING 1-10 OF 33 REFERENCES
The Stable marriage problem - structure and algorithms
TLDR
The authors develop the structure of the set of stable matchings in the stable marriage problem in a more general and algebraic context than has been done previously; they discuss the problem's structure in terms of rings of sets, which allows many of the most useful features to be seen as features of a moregeneral set of problems.
Stable Marriage and Indifference
Stable Marriage with Incomplete Lists and Ties
TLDR
This paper shows that the situation changes substantially if the problem not only becomes NP-hard, but also the optimal cost version has no approximation algorithm achieving the approximation ratio of N1-Ɛ, where N is the instance size, unless P=NP.
An efficient algorithm for the “optimal” stable marriage
TLDR
By exploiting the structure of the set of all stable matchings, and using graph-theoretic methods, an O(n4) algorithm for this problem is derived and achieves the objective of maximizing the average “satisfaction” of all people.
An Efficient Algorithm for the "Stable Roommates" Problem
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis
TLDR
The marriage model and the labor market for medical interns, a simple model of one seller and many buyers, and Discrete models with money, and more complex preferences are examined.
Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms
TLDR
This work states that existence of a stable matching: the fundamental algorithm and the principle of deferred decisions: coupon collecting and theoretical developments: application to the shortest path are true.
NP-Complete Stable Matching Problems
The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory
  • A. Roth
  • Economics
    Journal of Political Economy
  • 1984
The organization of the labor market for medical interns and residents underwent a number of changes before taking its present form in 1951. The record of these changes and the problems that prompted…
A New Fixed Point Approach for Stable Networks and Stable Marriages
  • T. Feder
  • Computer Science
    J. Comput. Syst. Sci.
  • 1992
...
...