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 \(2 - c{{\rm log N} \over {N}}\), 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 \(2 - c{{1} \over {\sqrt{N}}}\), where c is a constant such that \(c \leq {{1}\over{4\sqrt{6}}}\).
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Iwama, K., Miyazaki, S., Yamauchi, N. (2005). A ( \(2 - c{{1} \over {\sqrt{N}}}\))–Approximation Algorithm for the Stable Marriage Problem. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_90
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DOI: https://doi.org/10.1007/11602613_90
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