The popular matching and condensation problems under matroid constraints

Naoyuki Kamiyama ()
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Naoyuki Kamiyama: Kyushu University

Journal of Combinatorial Optimization, 2016, vol. 32, issue 4, No 19, 1305-1326

Abstract: Abstract The popular matching problem introduced by Abraham, Irving, Kavitha, and Mehlhorn is a matching problem in which there exist applicants and posts, and applicants have preference lists over posts. A matching M is said to be popular, if there exists no other matching N such that the number of applicants that prefer N to M is larger than the number of applicants that prefer M to N. The goal of this problem is to decide whether there exists a popular matching, and find a popular matching if one exists. In this paper, we first consider a matroid generalization of the popular matching problem with strict preference lists, 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 a matroid generalization of the popular matching problem with strict preference lists by deleting a minimum number of applicants so that it has a popular matching. This problem is a matroid generalization of the popular condensation problem with strict preference lists introduced by Wu, Lin, Wang, and Chao. By using the results in the first half, we give a polynomial-time algorithm for this problem.

Keywords: Popular matching; Popular condensation; Matroid (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9965-8

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