Three fast algorithms for four problems in stable marriage
SIAM Journal on Computing
An efficient algorithm for the “optimal” stable marriage
Journal of the ACM (JACM)
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
NP-complete stable matching problems
Journal of Algorithms
Stable marriage and indifference
CO89 Selected papers of the conference on Combinatorial Optimization
Approximation algorithms for NP-hard problems
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The Hospitals/Residents Problem with Ties
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Stable Marriage with Incomplete Lists and Ties
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Approximability results for stable marriage problems with ties
Theoretical Computer Science
Randomized approximation of the stable marriage problem
Theoretical Computer Science - Special papers from: COCOON 2003
Stable marriage with ties and bounded length preference lists
Journal of Discrete Algorithms
Brief announcement: a note on distributed stable matching
Proceedings of the 28th ACM symposium on Principles of distributed computing
Randomized approximation of the stable marriage problem
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
| Hi-index | 0.00 |
The stable marriage problem has received considerable attention both due to its practical applications as well as its mathematical structure. While the original problem has all participants ranka ll members of the opposite sex in a strict order of preference, two natural variations are to allow for incomplete preference lists and ties in the preferences. Both variations are polynomially solvable by a variation of the classical algorithm of Gale and Shapley. On the other hand, it has recently been shown to be NP-hard to find a maximum cardinality stable matching when both of the variations are allowed.We show here that it is APX-hard to approximate the maximum cardinality stable matching with incomplete lists and ties. This holds for some very restricted instances both in terms of lengths of preference lists, and lengths and occurrences of ties in the lists. We also obtain an optimal 驴(N) hardness results for 'minimum egalitarian' and 'minimum regret' variants.