Popular matchings with two-sided preferences and one-sided ties
Paper i proceeding, 2015

We are given a bipartite graph G = (A ∪ B, E) where each vertex has a preference list ranking its neighbors: in particular, every a ∈ A ranks its neighbors in a strict order of preference, whereas the preference lists of b ∈ B may contain ties. A matching M is popular if there is no matching M’ such that the number of vertices that prefer M’ to M exceeds the number that prefer M to M’. We show that the problem of deciding whether G admits a popular matching or not is NP-hard. This is the case even when every b ∈ B either has a strict preference list or puts all its neighbors into a single tie. In contrast, we show that the problem becomes polynomially solvable in the case when each b ∈ B puts all its neighbors into a single tie. That is, all neighbors of b are tied in b’s list and and b desires to be matched to any of them. Our main result is an O(n2) algorithm (where n = |A ∪ B|) for the popular matching problem in this model. Note that this model is quite different from the model where vertices in B have no preferences and do not care whether they are matched or not.


Á. Cseh

Technische Universität Berlin

Chien-Chung Huang

Chalmers, Data- och informationsteknik, Datavetenskap

T. Kavitha

Tata Institute of Fundamental Research

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 9134 367-379
978-3-662-47672-7 (ISBN)


Språkteknologi (språkvetenskaplig databehandling)





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