SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Dynamic matching markets and voting paths
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Pareto optimality in house allocation problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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
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
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
Efficient algorithms for weighted rank-maximal matchings and related problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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
ACM Transactions on Algorithms (TALG)
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We study the problem of assigning applicants to jobs. Each applicant has a weight and provides a preference list, which may contain ties, ranking a subset of the jobs. An applicant x may prefer one matching over the other (or be indifferent between them, in case of a tie) based on the jobs x gets in the two matchings and x's personal preference. A matching M is popular if there is no other matching M′ such that the weight of the applicants who prefer M′ over M exceeds the weight of those who prefer M over M′. We present two algorithms to find a popular matching, or in case none exists, to establish so. For the case of strict preferences we develop an O(n+m) time algorithm. When ties are allowed a more involved algorithm solves the problem in $O(\min(k \sqrt{n}, n) m)$ time, where k is the number of distinct weights the applicants are given.