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Strongly Stable Matchings under Matroid Constraints (2208.11272v3)
Published 24 Aug 2022 in cs.GT and econ.TH
Abstract: We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference of each agent may contain ties. In this setting, we consider the problem of checking the existence of a strongly stable matching, and finding a strongly stable matching if a strongly stable matching exists. We propose a polynomial-time algorithm for this problem.