The complexity of counting stable marriages
SIAM Journal on Computing
Three fast algorithms for four problems in stable marriage
SIAM Journal on Computing
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Lower bounds for the stable marriage problem and its variants
SIAM Journal on Computing
NP-complete stable matching problems
Journal of Algorithms
A necessary and sufficient condition for the existence of a complete stable matching
Journal of Algorithms
Stable networks and product graphs
Stable networks and product graphs
A new fixed point approach for stable networks and stable marriages
Journal of Computer and System Sciences
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
A New Approach to Stable Matching Problems
SIAM Journal on Computing
The set of super-stable marriages forms a distributive lattice
Discrete Applied Mathematics
Preference structures and their numerical representations
Theoretical Computer Science
Hard variants of stable marriage
Theoretical Computer Science
The stable roommates problem with ties
Journal of Algorithms
The structure of stable marriage with indifference
Discrete Applied Mathematics
Strong Stability in the Hospitals/Residents Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The stable marriage problem with restricted pairs
Theoretical Computer Science
Approximability results for stable marriage problems with ties
Theoretical Computer Science
On a generalization of the stable roommates problem
ACM Transactions on Algorithms (TALG)
Note: An algorithm for a super-stable roommates problem
Theoretical Computer Science
Hi-index | 5.23 |
We consider a generalization of the Stable Roommates problem (sr), in which preference lists may be partially ordered and forbidden pairs may be present, denoted by srpf. This includes, as a special case, a corresponding generalization of the classical Stable Marriage problem (sm), denoted by smpf. By extending previous work of Feder, we give a two-step reduction from srpf to 2-sat. This has many consequences, including fast algorithms for a range of problems associated with finding ''optimal'' stable matchings and listing all solutions, given variants of sr and sm. For example, given an smpf instance I, we show that there exists an O(m) ''succinct'' certificate for the unsolvability of I, an O(m) algorithm for finding all the super-stable pairs in I, an O(m+kn) algorithm for listing all the super-stable matchings in I, an O(m^1^.^5) algorithm for finding an egalitarian super-stable matching in I, and an O(m) algorithm for finding a minimum regret super-stable matching in I, where n is the number of men, m is the total length of the preference lists, and k is the number of super-stable matchings in I. Analogous results apply in the case of srpf.