| Abstract Popular Matchings (2008) | |||||||||||||
Abstract | |||||||||||||
| We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in order of preference, possibly involving ties. We say that a matching M is popular if there is no matching M ' such that the nnmber of applicants preferring M ~ to M- exceeds the number of applicants preferring M to M-'. In this paper, we give the first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists. For the special case in which every preference list is strictly ordered (i.e. contains no ties), we give an O(n+m) time algorithm, where n is the total number of applicants and posts, and m is the total length of all the preference lists. For the general case in which preference lists may contain ties, we give an O(x/n'm) time algorithm, and show that the problem has equivalent time complexity to the maxinmm-cardinality bipartite matching problem. 1 | |||||||||||||
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