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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A preliminary version of this paper was presented at the 16th Annual International Symposium on Algorithms and Computation, ISAAC 2005.
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Iwama, K., Miyazaki, S. & Yamauchi, N. A ( \(2-c\frac{1}{\sqrt{N}}\) )-Approximation Algorithm for the Stable Marriage Problem. Algorithmica 51, 342–356 (2008). https://doi.org/10.1007/s00453-007-9101-y
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DOI: https://doi.org/10.1007/s00453-007-9101-y