The complexity of counting stable marriages
SIAM Journal on Computing
The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
NP-complete stable matching problems
Journal of Algorithms
On-line algorithms for weighted bipartite matching and stable marriages
Theoretical Computer Science
Hard variants of stable marriage
Theoretical Computer Science
The stable roommates problem with ties
Journal of Algorithms
Matching Medical Students to Pairs of Hospitals: A New Variation on a Well-Known Theme
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Two algorithms for the Student-Project Allocation problem
Journal of Discrete Algorithms
“Almost stable” matchings in the roommates problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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Given an instance I of the classical Stable Marriage problem with Incomplete preference lists (smi), a maximum cardinality matching can be larger than a stable matching. In many large-scale applications of smi, we seek to match as many agents as possible. This motivates the problem of finding a maximum cardinality matching in I that admits the smallest number of blocking pairs (so is “as stable as possible”). We show that this problem is NP-hard and not approximable within n 1 − ε , for any ε 0, unless P=NP, where n is the number of men in I. Further, even if all preference lists are of length at most 3, we show that the problem remains NP-hard and not approximable within Δ, for some Δ 1. By contrast, we give a polynomial-time algorithm for the case where the preference lists of one sex are of length at most 2.