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
Two algorithms for the Student-Project Allocation problem
Journal of Discrete Algorithms
An improved approximation lower bound for finding almost stable maximum matchings
Information Processing Letters
“Almost stable” matchings in the roommates problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
The hospitals/residents problem with quota lower bounds
ESA'11 Proceedings of the 19th European conference on Algorithms
Popularity vs maximum cardinality in the stable marriage setting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
“Almost stable” matchings in the Roommates problem with bounded preference lists
Theoretical Computer Science
Popular matchings in the stable marriage problem
Information and Computation
Socially stable matchings in the hospitals/residents problem
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
| Hi-index | 5.23 |
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^-^@e, for any @e0, 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 @d, for some @d1. By contrast, we give a polynomial-time algorithm for the case where the preference lists of one sex are of length at most 2. We also extend these results to the cases where (i) preference lists may include ties, and (ii) we seek to minimize the number of agents involved in a blocking pair.