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
SIAM Journal on Discrete Mathematics
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
On the complexity of stable matchings with and without ties
On the complexity of stable matchings with and without ties
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
A Constraint Programming Approach to the Stable Marriage Problem
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
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
Two algorithms for the Student-Project Allocation problem
Journal of Discrete Algorithms
Many-to-One Stable Matching: Geometry and Fairness
Mathematics of Operations Research
Improved approximation results for the stable marriage problem
ACM Transactions on Algorithms (TALG)
Efficient algorithms for generalized Stable Marriage and Roommates problems
Theoretical Computer Science
A 1.875: approximation algorithm for the stable marriage problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A Constraint Programming Approach to the Hospitals / Residents Problem
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Better and Simpler Approximation Algorithms for the Stable Marriage Problem
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
The stable marriage problem with master preference lists
Discrete Applied Mathematics
Size Versus Stability in the Marriage Problem
Approximation and Online Algorithms
Stable marriage with ties and bounded length preference lists
Journal of Discrete Algorithms
Finding large stable matchings
Journal of Experimental Algorithmics (JEA)
A 3/2-Approximation Algorithm for General Stable Marriage
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Size versus stability in the marriage problem
Theoretical Computer Science
Randomized approximation of the stable marriage problem
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
The stable roommates problem with globally-ranked pairs
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
The College Admissions problem with lower and common quotas
Theoretical Computer Science
A 25/17-approximation algorithm for the stable marriage problem with one-sided ties
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Local search for stable marriage problems with ties and incomplete lists
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
A (2 - c1/√N)-approximation algorithm for the stable marriage problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A specialised binary constraint for the stable marriage problem
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Mechanisms for the marriage and the assignment game
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Popular matchings in the marriage and roommates problems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Communication requirements for stable marriages
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Faster and simpler approximation of stable matchings
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Finding All Stable Pairs and Solutions to the Many-to-Many Stable Matching Problem
INFORMS Journal on Computing
Stable assignment with couples: Parameterized complexity and local search
Discrete Optimization
An 8/5-approximation algorithm for a hard variant of stable marriage
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Complexity of the resource allocation/matching problem with weight based ceilings
ICA3PP'12 Proceedings of the 12th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
On finding better friends in social networks
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
(Re)Configuration using web data: a case study on the reviewer assignment problem
RR'12 Proceedings of the 6th international conference on Web Reasoning and Rule Systems
Cyclic stable matching for three-sided networking services
Computer Networks: The International Journal of Computer and Telecommunications Networking
Two-sided matching with partial information
Proceedings of the fourteenth ACM conference on Electronic commerce
Stable marriage and roommate problems with individual-based stability
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Modeling stable matching problems with answer set programming
RuleML'13 Proceedings of the 7th international conference on Theory, Practice, and Applications of Rules on the Web
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The Stable Marriage Problem and its many variants have been widely studied in the literature (Gusfield and Irving, The Stable Marriage Problem: Structure and Algorithms, MIT Press, Cambridge, MA, 1989; Roth and Sotomayor, Two-sided matching: a study in game-theoretic modeling and analysis, Econometric Society Monographs, vol. 18, Cambridge University Press, Cambridge, 1990; Knuth, Stable Marriage and its Relation to Other Combinatorial Problems, CRM Proceedings and Lecture Notes, vol. 10, American Mathematical Society, Providence, RI, 1997), partly because of the inherent appeal of the problem, partly because of the elegance of the associated structures and algorithms, and partly because of important practical applications, such as the National Resident Matching Program (Roth, J. Political Economy 92(6) (1984) 991) and similar large-scale matching schemes. Here, we present the first comprehensive study of variants of the problem in which the preference lists of the participants are not necessarily complete and not necessarily totally ordered. We show that, under surprisingly restrictive assumptions, a number of these variants are hard, and hard to approximate. The key observation is that, in contrast to the case where preference lists are complete or strictly ordered (or both), a given problem instance may admit stable matchings of different sizes. In this setting, examples of problems that are hard are: finding a stable matching of maximum or minimum size, determining whether a given pair is stableeven if the indifference takes the form of ties on one side only, the ties are at the tails of lists, there is at most one tie per list, and each tie is of length 2; and finding, or approximating, both an `egalitarian' and a `minimum regret' stable matching. However, we give a 2-approximation algorithm for the problems of finding a stable matching of maximum or minimum size. We also discuss the significant implications of our results for practical matching schemes.