Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
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
SIAM Journal on Computing
Bounded Unpopularity Matchings
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Popular Matchings with Variable Job Capacities
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Popular matchings with variable item copies
Theoretical Computer Science
SIAM Journal on Discrete Mathematics
Popular matchings in the stable marriage problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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 stable marriage problem
Information and Computation
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We study the problem of matching applicants to jobs under one-sided preferences; that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties. A matching M is said to be more popular than T if the applicants that prefer M to T outnumber those that prefer T to M . A matching is said to be popular if there is no matching more popular than it. Equivalently, a matching M is popular if *** (M ,T ) *** *** (T ,M ) for all matchings T , where *** (X ,Y ) is the number of applicants that prefer X to Y . Previously studied solution concepts based on the popularity criterion are either not guaranteed to exist for every instance (e.g., popular matchings) or are NP-hard to compute (e.g., least unpopular matchings). This paper addresses this issue by considering mixed matchings. A mixed matching is simply a probability distributions over matchings in the input graph. The function *** that compares two matchings generalizes in a natural manner to mixed matchings by taking expectation. A mixed matching P is popular if *** (P ,Q ) *** *** (Q ,P ) for all mixed matchings Q . We show that popular mixed matchings always exist and we design polynomial time algorithms for finding them. Then we study their efficiency and give tight bounds on the price of anarchy and price of stability of the popular matching problem.