Many-to-One Popular Matchings with Two-Sided Preferences and One-Sided Ties

Gopal, Kavitha; Nasre, Meghana; Nimbhorkar, Prajakta; Reddy, T. Pradeep

doi:10.1007/978-3-030-26176-4_16

Cited by 1 publication

(1 citation statement)

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“…Popular matchings Popularity as an optimality principle has been on the rise recently [19,25,30] in the matchings under preferences literature. On instances with two-sided preferences, Brandl and Kavitha [12] and Gopal et al [28] studied popularity for many-to-many and many-to-one matching problems with upper quotas only. For the model introduced in the latter paper, the complexity of deciding whether a popular matching exists is still open.…”

Section: Related Workmentioning

confidence: 99%

Pareto optimal and popular house allocation with lower and upper quotas

Cseh¹,

Friedrich²,

Peters³

2021

Preprint

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In the house allocation problem with lower and upper quotas, we are given a set of applicants and a set of projects. Each applicant has a strictly ordered preference list over the projects, while the projects are equipped with a lower and an upper quota. A feasible matching assigns the applicants to the projects in such a way that a project is either matched to no applicant or to a number of applicants between its lower and upper quota. In this model we study two classic optimality concepts: Pareto optimality and popularity. We show that finding a popular matching is hard even if the maximum lower quota is 2 and that finding a perfect Pareto optimal matching, verifying Pareto optimality, and verifying popularity are all NP-complete even if the maximum lower quota is 3. We complement the last three negative results by showing that the problems become polynomial-time solvable when the maximum lower quota is 2, thereby answering two open questions of Cechlárová and Fleiner [17]. Finally, we also study the parameterized complexity of all four mentioned problems.

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