The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Handbook of combinatorics (vol. 1)
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Popular matchings in the capacitated house allocation problem
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A 1.875: approximation algorithm for the stable marriage problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Reducing rank-maximal to maximum weight matching
Theoretical Computer Science
Bounded Unpopularity Matchings
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Matchings in graphs variations of the problem
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
The stable roommates problem with globally-ranked pairs
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Popular matchings: structure and algorithms
Journal of Combinatorial Optimization
Dynamic matching markets and voting paths
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
A (2 - c1/√N)-approximation algorithm for the stable marriage problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Efficient algorithms for weighted rank-maximal matchings and related problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in order of preference, possibly involving ties. We say that a matching M is popular if there is no matching M' such that the number of applicants preferring M' to M exceeds the number of applicants preferring M to M'. In this paper, we give the first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists. For the special case in which every preference list is strictly ordered (i.e. contains no ties), we give an O(n+m) time algorithm, where n is the total number of applicants and posts, and m is the total length of all the preference lists. For the general case in which preference lists may contain ties, we give an O(√nm) time algorithm, and show that the problem has equivalent time complexity to the maximum-cardinality bipartite matching problem.