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A necessary and sufficient condition for the existence of a complete stable matching

Jimmy J. M. Tan
- 02 Jan 1991 - 
- Vol. 12, Iss: 1, pp 154-178
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TLDR
A new structure called a “stable partition” is defined, which generalizes the notion of a complete stable matching, and it is proved that every instance of the stable roommates problem has at least one such structure.
About: 
This article is published in Journal of Algorithms.The article was published on 1991-01-02 and is currently open access. It has received 198 citations till now. The article focuses on the topics: Stable roommates problem & Stable marriage problem.

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Citations
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Proceedings ArticleDOI

Self-Stabilization in Preference-Based Networks

Fabien Mathieu
TL;DR: This paper investigates the speed and quality of the convergence process with respect to the model parameters and provides insight into the design of system parameters, such as the number of connections or the algorithm for choosing new partners.
Journal ArticleDOI

Competitive equilibrium and singleton cores in generalized matching problems

Jaeok Park
- 01 May 2017 - 
TL;DR: It is shown that a competitive matching exists if and only if the matching produced by the top trading cycles algorithm is feasible, in which case it is the unique competitive matching, and the core is a singleton consisting of the competitive matching.
Proceedings ArticleDOI

The Stable Configuration of Acyclic Preference-Based Systems

Fabien Mathieu, +2 more
TL;DR: Using random overlay graphs, it is proved by means of a mean-field assumption and a fluid-limit technique that acyclic systems have an asymptotically continuous independent rank distribution for a proper scaling, and the analytical solution is compared to simulations.
Dissertation

Scarf's Theorem and Applications in Combinatorics

Caroline Rioux
TL;DR: In this paper, it was shown that for a proper labeling of the vertices in a simplicial subdivision of an n-simplex, there exists at least one elementary simplex which carries all labels {0, 1,..., n}.
Journal ArticleDOI

Moral hazard and stability

Norovsambuu Tumennasan
- 13 Feb 2014 - 
TL;DR: It is demonstrated that carefully designed contracts are sometimes the reason why teams do not form, and if the team members cannot make transfers, then moral hazard affects stability positively in a large class of games.
References
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Journal ArticleDOI

College Admissions and the Stability of Marriage

David Gale, +1 more
- 01 Jan 1962 - 
TL;DR: In this article, the authors studied the relationship between college admission and the stability of marriage in the United States, and found that college admission is correlated with the number of stable marriages.
Book

The Stable Marriage Problem: Structure and Algorithms

Dan Gusfield, +1 more
TL;DR: 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.
Journal ArticleDOI

Some remarks on the stable matching problem

David Gale, +1 more
- 01 Jul 1985 - 
TL;DR: Three results on properties of these matchings are established and two short proofs of a recent theorem of Dubins and Freedman are presented.
Journal ArticleDOI

An efficient algorithm for the “stable roommates” problem

Robert W. Irving
- 01 Dec 1985 - 
TL;DR: An O(n2) algorithm is described that will determine, for any instance of the stable marriage problem, whether a stable matching exists, and if so, will find such a matching.
Journal ArticleDOI

The stable marriage problem

D. G. McVitie, +1 more
- 01 Jul 1971 - 
TL;DR: The original work of Gale and Shapley on an assignment method using the stable marriage criterion has been extended and the algorithm derived is proved to satisfy all the conditions of the problem.
Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "A necessary and sufficient condition for the existence of a complete stable matching" ?

In this paper, the authors give a necessary and sufficient condition for the existence of a complete stable matching ; namely, the non-existence of any odd party, which will be defined subsequently. The authors define a new structure called a “ stable partition, ” which generalizes the notion of a complete stable matching, and prove that every instance of the stable roommates problem has at least one such structure. The authors also show that a stable partition contains all the odd parties, if there are any.