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Cseh, Ágnes
Kavitha, Telikepalli
Year of Publication: 
Series/Report no.: 
IEHAS Discussion Papers MT-DP - 2017/25
Given a bipartite graph G=(A B, E) with strict preference lists and given an edge e E, we ask if there exists a popular matching in G that contains e. We call this the popular edge problem. A matching M is popular if there is no matching M' such that the vertices that prefer M' to M outnumber those that prefer M to M'. It is known that every stable matching is popular; however G may have no stable matching with the edge e. In this paper we identify another natural subclass of popular matchings called "dominant matchings" and show that if there is a popular matching that contains the edge e, then there is either a stable matching that contains e or adominant matching that contains e. This allows us to design a linear time algorithm for identifying the set of popular edges. When preference lists are complete, we show an O(n3) algorithm to find a popular matching containing a given set of edges or report that none exists, where n =+
popular matching
matching under preferences
dominant matching
Document Type: 
Working Paper
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