An approximation algorithm for the stable marriage problem with ties of length two

摘要

While the original stable marriage problem requires all participants to rank all members of the opposite sex in a strict order, two natural variations are to allow for incomplete preference lists and ties in the preferences. Either variation is polynomially solvable, but it has recently been shown to be NP-hard to find a maximum cardinality stable matching when both of the variations are allowed. It is easy to see that the size of any two stable matchings differ by at most a factor of two, and so, approximation of factor two is trivial. In this paper, we give a first nontrivial result for approximation of factor less than two. Our algorithm achieves a factor of 25/13(＜ 1.924) for a restricted case where each tie is of length two.