Abstract
An input to the POPULAR MATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the POPULAR MATCHING problem the objective is to test whether there exists a matching M* such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M*. In this article, we settle the computational complexity of the POPULAR MATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.
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Index Terms
Popular Matching in Roommates Setting Is NP-hard
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Popular matching in roommates setting is NP-hard
SODA '19: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete AlgorithmsAn input to the Popular Matching problem, in the roommates setting, consists of a graph G where each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there exists a ...
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