ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Note: Optimal popular matchings
Discrete Applied Mathematics
Popular Matchings: Structure and Algorithms
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Popular Matchings with Variable Job Capacities
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Social Networks and Stable Matchings in the Job Market
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Popular matchings in the weighted capacitated house allocation problem
Journal of Discrete Algorithms
Popular matchings with variable item copies
Theoretical Computer Science
SIAM Journal on Discrete Mathematics
Theoretical Computer Science
An experimental comparison of single-sided preference matching algorithms
Journal of Experimental Algorithmics (JEA)
Popular matchings in the stable marriage problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Social welfare in one-sided matching markets without money
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Near-popular matchings in the roommates problem
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
Popular matchings in the marriage and roommates problems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Popular matchings in the stable marriage problem
Information and Computation
Welfare maximization and truthfulness in mechanism design with ordinal preferences
Proceedings of the 5th conference on Innovations in theoretical computer science
ACM Transactions on Algorithms (TALG)
Discrete Applied Mathematics
Journal of Combinatorial Optimization
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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 nonempty 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 of the preference lists. For the general case in which preference lists may contain ties, we give an $O(\sqrt{n}m)$ time algorithm.