I have a slightly different formulation of the stable marriage problem. Basically, I can match one man to one woman, but the preference list is incomplete, which means that a man has expressed interest only in a subset of women and vice versa. I don't think the original Gale Shapley algorithm would work for this, if so what modifications do I need to make? If Gale Shapely does not work here, is there any algorithm to solve this? code suggestions, especially in python for this kind of problem, are very welcomed.
Men = [1, 2, 3, 4, 5] Women = [a, b, c, d, e] preferences: men: 1: a, c, d 2: d, a, b 3: a, e, b 4: c, a, d 5: e, d, a women: a: 1, 3, 4 b: 4, 2, 5 c: 5, 1, 4 d: 3, 2, 1 e: 5, 3, 1
I need to match each man to one and only one woman
and the number of preferences allowed is fixed and less than the number of candidates.