Abstract

We consider the problem of finding a stable matching of maximum size when both ties and unacceptable partners are allowed in preference lists. This problem is NP-hard and the current best known approximation algorithm achieves the approximation ratio 2−c(log N)/N, where c is an arbitrary positive constant and N is the number of men in an input. In this paper, we improve the ratio to $2-c/\sqrt{N}$, where c is an arbitrary constant that satisfies $c\leq 1/{(4\sqrt{6})}$.

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