Abstract
The input is a bipartite graph where each vertex ranks its neighbors in a strict order of preference. A matching M * is said to be popular if there is no matching M such that more vertices are better off in M than in M *. We consider the problem of computing a maximum cardinality popular matching in G. It is known that popular matchings always exist in such an instance G, however the complexity of computing a maximum cardinality popular matching was not known so far. In this paper we give a simple characterization of popular matchings when preference lists are strict and a sufficient condition for a maximum cardinality popular matching. We then show an O(mn 0) algorithm for computing a maximum cardinality popular matching in G, where m = |E| and . © 2011 Springer-Verlag.
Cite
CITATION STYLE
Huang, C. C., & Kavitha, T. (2011). Popular matchings in the stable marriage problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6755 LNCS, pp. 666–677). https://doi.org/10.1007/978-3-642-22006-7_56
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