Popular Mixed Matchings

13 years 11 months ago

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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 φ(M, T) ≥ φ(T, M) for all matchings T, where φ(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 distribution over matchings in the input graph. The function φ that compares two matchings generalizes in a natural manner to mixed matchings...

Telikepalli Kavitha, Julián Mestre, Meghana

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