Journal ArticleDOI
Linear programming brings marital bliss
TLDR
In this article, the authors describe the convex hull of the incidence vectors of stable matchings and propose a linear program to solve the optimal stable marriage problem as a linear programming problem.About:
This article is published in Operations Research Letters.The article was published on 1989-06-01. It has received 184 citations till now. The article focuses on the topics: Stable marriage problem & Linear programming.read more
Citations
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Two-Sided Matching
Alvin E. Roth,Marilda Sotomayor +1 more
TL;DR: A comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching can be found in this paper, where the focus is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized.
Book
Algorithmics of Matching Under Preferences
TL;DR: This book builds on the author’s prior research in this area, and also his practical experience of developing algorithms for matching kidney patients to donors in the UK, for assigning medical students to hospitals in Scotland, and for allocating students to elective courses and projects.
Journal ArticleDOI
A fixed-point approach to stable matchings and some applications
TL;DR: A matroid-generalization of the stable marriage theorem is formulated and results of Vande Vate and Rothblum are extended on the bipartite stable matching polytope and the lattice structure of generalized stable matchings are studied.
Journal ArticleDOI
The Geometry of Fractional Stable Matchings and its Applications
Chung-Piaw Teo,Jay Sethuraman +1 more
TL;DR: It is shown that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions, which leads to a genuinely simple proof of the integrality of the stablemarriage polytopes.
Journal ArticleDOI
Stable Matchings, Optimal Assignments, and Linear Programming
TL;DR: It is shown that those fractional matchings in the Stable Marriage Polytope form a lattice with respect to a partial ordering that involves stochastic dominance, and all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons.
References
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Linear Programming and Extensions
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
Journal ArticleDOI
College Admissions and the Stability of Marriage
David Gale,Lloyd S. Shapley +1 more
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 theory of committees and elections
TL;DR: In this paper, Dodgson's Third Pamphlet 'A Method...' (1876) was used to discuss the Elasticity of Committee Decisions with an Altering Size of Majority.
Book
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis
Alvin E. Roth,Marilda Sotomayor +1 more
TL;DR: 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.