The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
NP-complete stable matching problems
Journal of Algorithms
A necessary and sufficient condition for the existence of a complete stable matching
Journal of Algorithms
SIAM Journal on Discrete Mathematics
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
A sublinear parallel algorithm for stable matching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Hard variants of stable marriage
Theoretical Computer Science
On the complexity of stable matchings with and without ties
On the complexity of stable matchings with and without ties
A new fixed point approach for stable networks stable marriages
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Stable partitions with W-preferences
Discrete Applied Mathematics
Discrete Applied Mathematics
A genetic algorithm for the project assignment problem
Computers and Operations Research
On a generalization of the stable roommates problem
ACM Transactions on Algorithms (TALG)
Efficient algorithms for generalized Stable Marriage and Roommates problems
Theoretical Computer Science
The stable fixtures problem-A many-to-many extension of stable roommates
Discrete Applied Mathematics
On the stable b-matching problem in multigraphs
Discrete Applied Mathematics
Genetic algorithm for the training time assignment problem of core laboratories
ICAI'08 Proceedings of the 9th WSEAS International Conference on International Conference on Automation and Information
Information Processing Letters
Size Versus Stability in the Marriage Problem
Approximation and Online Algorithms
Size versus stability in the marriage problem
Theoretical Computer Science
The stable roommates problem with globally-ranked pairs
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Upper bounds for stabilization in acyclic preference-based systems
SSS'07 Proceedings of the 9h international conference on Stabilization, safety, and security of distributed systems
Expert Systems with Applications: An International Journal
Note: An algorithm for a super-stable roommates problem
Theoretical Computer Science
Distributed stable matching problems with ties and incomplete lists
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
“Almost stable” matchings in the roommates problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
A specialised binary constraint for the stable marriage problem
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Stable assignment with couples: Parameterized complexity and local search
Discrete Optimization
Acyclic preference systems in p2p networks
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
Complementary cooperation, minimal winning coalitions, and power indices
Theoretical Computer Science
Two-sided matching with partial information
Proceedings of the fourteenth ACM conference on Electronic commerce
Two hardness results for core stability in hedonic coalition formation games
Discrete Applied Mathematics
| Hi-index | 0.01 |
We study the variant of the well-known stable roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear-time algorithm for finding a super-stable matching if one exists, given a stable roommates instance with ties. This contrasts with the known NP-hardness of the analogous problem under weak stability. We also extend our algorithm to cope with preference lists that are incomplete and/or partially ordered. On the other hand, for a given stable roommates instance with ties and incomplete lists, we show that the weakly stable matchings may be of different sizes and the problem of finding a maximum cardinality weakly stable matching is NP-hard, though approximable within a factor of 2.