An Optimal Algorithm for the Popular Condensation Problem

A Matroid Generalization of the Super-Stable Matching Problem

“…More precisely, in this paper, we consider the problem of modifying an instance of the super-stable matching problem by deleting some bounded number of agents in such a way that there exists a super-stable matching in the modified instance. Similar problems for popular matchings were considered in [15,16].…”

Popular Matchings with Ties and Matroid Constraints

“…Abraham, Irving, Kavitha, and Mehlhorn [1] presented polynomial-time algorithms for the popular matching problem with/without ties. Since their seminal paper, several variations of the popular matching problem [12,19,21,24] and related problems [12,13,14,15,16,20,25,26] have been investigated.…”

The Popular Matching and Condensation Problems Under Matroid Constraints

“…These problems have been shown to be hard in general. Wu, Lin, Wang, and Chao [15] considered the problem of transforming the set of agents so that a given instance admits a popular matching. More precisely, they introduced the popular condensation problem whose goal is to transform a given instance so that it has a popular matching by deleting a minimum number of agents, and gave a polynomial-time algorithm for this problem.…”

“…In this paper, we consider a matroid generalization of the popular condensation problem (i.e., the popular condensation problem in the matroid setting presented by Kamiyama [6]), and give a polynomial-time algorithm for this problem. Our algorithm can be regarded as a matroid generalization of the algorithm presented by Wu, Lin, Wang, and Chao [15].…”