Popular edges and dominant matchings

Popular Edges and Dominant Matchings

Given a bipartite graph G = (A∪B,E) with strict preference lists and e∗ ∈ E, we ask if there exists a popular matching in G that contains the edge 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 sta...

Popular Matchings

Popular and Clan-Popular b-Matchings

Suppose that each member of a set of agents has a preference list of a subset of houses, possibly involving ties, and each agent and house has their capacity denoting the maximum number of houses/agents (respectively) that can be matched to him/her/it. We want to find a matching M , called popular, for which there is no other matching M ′ such that more agents prefer M ′ to M than M to M ′, sub...

Optimal popular matchings

In this paper we consider the problem of computing an ‘‘optimal’’ popular matching. We assume that our input instance G = (A∪P , E1 ∪̇ · · · ∪̇ Er ) admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness inwhich cas...

Popular Matchings: Structure and Algorithms

An instance of the popular matching problem (POP-M) consists of a set of applicants and a set of posts. Each applicant has a preference list that strictly ranks a subset of the posts. A matching M of applicants to posts is popular if there is no other matching M ′ such that more applicants prefer M ′ to M than prefer M to M . Abraham et al [1] described a linear time algorithm to determine whet...