The Roommates Problem Discussed

The stable roommates problem as originally posed by Gale and Shapley [1] in 1962 involves a single set of even cardinality 2n, each member of which ranks every other member in order of preference. A stable matching is then a partition of this single set into n pairs such that no two unmatched members both prefer each other to their partners under the matching. However, a simple counterexample quickly proves that a stable matching need not exist in the stable roommates problem. In 1984, Irving published an algorithm that determines in polynomial time if a stable matching is possible on a given set, and if so, finds such a matching. However, others have made efforts to redefine the concept of a “stable matching,” or even reframe the problem altogether to give it new real-world significance. The present paper describes both Irving’s algorithm, and look at other reappraisals of this problem.