Integer Programming and Arrovian Social Welfare Functions
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Integer programming and arrovian social welfare functions
Mathematics of Operations Research
Many-to-One Stable Matching: Geometry and Fairness
Mathematics of Operations Research
Sampling stable marriages: why spouse-swapping won't work
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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 generalized median stable matchings: finding them is not that easy
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
The College Admissions problem with lower and common quotas
Theoretical Computer Science
Monotonicity in bargaining networks
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A 25/17-approximation algorithm for the stable marriage problem with one-sided ties
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Center stable matchings and centers of cover graphs of distributive lattices
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
SIAM Journal on Discrete Mathematics
Mathematics of Operations Research
Note: Blockers and antiblockers of stable matchings
Theoretical Computer Science
| Hi-index | 0.00 |
We study the classical stable marriage and stable roommates problems using a polyhedral approach. We propose a new LP formulation for the stable roommates problem, which has a feasible solution if and only if the underlying roommates problem has a stable matching. Furthermore, for certain special weight functions on the edges, we construct a 2-approximation algorithm for the optimal stable roommates problem. Our technique exploits features of the geometry of fractional solutions of this formulation. For the stable marriage problem, we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions. This also leads to a genuinely simple proof of the integrality of the stable marriage polytope.