Marriage, honesty, and stability
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Popular matchings in the capacitated house allocation problem
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Bounded Unpopularity Matchings
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
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
Popular matchings: structure and algorithms
Journal of Combinatorial Optimization
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
Dynamic matching markets and voting paths
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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)
Journal of Combinatorial Optimization
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We consider matching markets where a centralized authority must find a matching between the agents on one side of the market, and the items on the other side. Such settings occur, for example, in mail-based DVD rental services such as NetFlix or in some job markets. The objective is to find a popular matching, or a matching that is preferred by a majority of the agents to any other matching. This concept was first defined and studied by Abraham et al. The main drawback of this concept is that popular matchings sometimes do not exist. We partially address this issue in this paper, by proving that in a probabilistic setting where preference lists are drawn at random and the number of items is more than the number of agents by a small multiplicative factor, popular matchings almost surely exist. More precisely, we prove that there is a threshold α ≈ 1.42 such that if the number of items divided by the number of agents exceeds this threshold, then a solution almost always exists. Our proof uses a characterization result by Abraham et al., and a number of tools from the theory of random graphs and phase transitions.