The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Characterization of stable matchings as extreme points of a polytope
Mathematical Programming: Series A and B
Stable matchings, optimal assignments, and linear programming
Mathematics of Operations Research
A new fixed point approach for stable networks and stable marriages
Journal of Computer and System Sciences
A New Approach to Stable Matching Problems
SIAM Journal on Computing
Discrete Applied Mathematics
The Geometry of Fractional Stable Matchings and its Applications
Mathematics of Operations Research
Many-to-many matching: stable polyandrous polygamy (or polygamous polyandry)
Discrete Applied Mathematics
Stable Networks and Product Graphs
Stable Networks and Product Graphs
Hard variants of stable marriage
Theoretical Computer Science
Refined Inequalities for Stable Marriage
Constraints
A fixed-point approach to stable matchings and some applications
Mathematics of Operations Research
A unified approach to finding good stable matchings in the hospitals/residents setting
Theoretical Computer Science
Finding a Level Ideal of a Poset
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
The stable roommates problem with choice functions
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Stable matching with couples: An empirical study
Journal of Experimental Algorithmics (JEA)
Mathematics of Operations Research
Note: Blockers and antiblockers of stable matchings
Theoretical Computer Science
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Baïou and Balinski characterized the stable admissions polytope using a system of linear inequalities. The structure of feasible solutions to this system of inequalities---fractional stable matchings---is the focus of this paper. The main result associates a geometric structure with each fractional stable matching. This insight appears to be interesting in its own right, and can be viewed as a generalization of the lattice structure (for integral stable matchings) to fractional stable matchings. In addition to obtaining simple proofs of many known results, the geometric structure is used to prove the following two results: First, it is shown that assigning each agent their “median” choice among all stable partners results in a stable matching, which can be viewed as a “fair” compromise; second, sufficient conditions are identified under which stable matchings exist in a problem with externalities, in particular, in the stable matching problem with couples.