Abstract
In this paper, we first consider a matroid generalization of the popular matching problem (without ties) introduced by Abraham, Irving, Kavitha, and Mehlhorn, and give a polynomial-time algorithm for this problem. In the second half of this paper, we consider the problem of transforming a given instance of the popular matching problem (without ties) by deleting a minimum number of applicants so that it has a popular matching under matroid constraints. This problem is a matroid generalization of the popular condensation problem proposed by Wu, Lin, Wang, and Chao. By using the results in the first half, we give a polynomial-time algorithm for this problem.
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