The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Transformation from arbitrary matchings to stable matchings
Journal of Combinatorial Theory Series A
The complexity of economic equilibria for house allocation markets
Information Processing Letters
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
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
Popular Matchings: Structure and Algorithms
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Popular matchings in the weighted capacitated house allocation problem
Journal of Discrete Algorithms
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Popular matchings: structure and algorithms
Journal of Combinatorial Optimization
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
ACM Transactions on Algorithms (TALG)
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We consider a matching market, in which the aim is to maintain a popular matching between a set of applicants and a set of posts, where each applicant has a preference list that ranks some subset of acceptable posts. The setting is dynamic: applicants and posts can enter and leave the market, and applicants can also change their preferences arbitrarily. After any change, the current matching may no longer be popular, in which case, we are required to update it. However, our model demands that we can switch from one matching to another only if there is consensus among the applicants to agree to the switch. Hence, we need to update via a voting path, which is a sequence of matchings, each more popular than its predecessor, that ends in a popular matching. In this paper, we show that, as long as some popular matching exists, there is a 2-step voting path from any given matching to some popular matching. Furthermore, given any popular matching, we show how to find a shortest-length such voting path in linear time