Abstract
A stable matching for an instance of the stable marriages problem or the stable roommates problem is bistable if it is also a stable matching when the ordering of the input preference lists is reversed. For the stable marriages problem, it is shown that the bistable matchings are a sublattice of the distributive lattice of stable matchings. In addition, the Gale–Shapley algorithm is modified to find the man-optimal bistable matching and to determine the irreducible bistable matchings.
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