TL;DR
This paper investigates the problem of assigning jobs to applicants with preferences and weights, introducing efficient algorithms to find popular matchings where no alternative matching is preferred by a higher weighted group.
Contribution
It provides the first efficient algorithms for finding popular matchings in weighted applicant-job assignment problems.
Findings
Algorithms efficiently find popular matchings when they exist.
Characterization of conditions under which popular matchings are possible.
Improved understanding of weighted preference-based matchings.
Abstract
We study the problem of assigning jobs to applicants. Each applicant has a weight and provides a preference list ranking a subset of the jobs. 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'. This paper gives efficient algorithms to find a popular matching if one exists.
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