Marriage and Roommate
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This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance I is a stable matching (that however must satisfy a certain condition) of some marriage instance I'. I' is obtained just by making two copies of I, one for the men's table and the other for the women's table. The second objective is to investigate the possibility of reducing the roommate problem to the marriage problem (with a one-to-one correspondence between their stable matchings) in polynomial time. For a given I, we construct the rotation POSET P of I' and then we “halve” it to obtain P', by which we can forget the above condition and can use all the closed subsets of P' for all the stable matchings of I. Unfortunately, this approach works (runs in polynomial time) only for restricted instances.
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