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arXiv · 1808.04510

On the approximability of the stable matching problem with ties of size two

Robert Chiang·Kanstantsin Pashkovich
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Abstract

The stable matching problem is one of the central problems of algorithmic game theory. If participants are allowed to have ties, the problem of finding a stable matching of maximum cardinality is an NP-hard problem, even when the ties are of size two. Moreover, in this setting it is UGC-hard to provide an approximation for the maximum cardinality stable matching problem with a constant factor smaller than 4/3. In this paper, we give a tight analysis of an approximation algorithm given by Huang and Kavitha for the maximum cardinality stable matching problem with ties of size two, demonstrating an improved 4/3-approximation factor.

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Robert Chiang, Kanstantsin Pashkovich. 2018-08-14. On the approximability of the stable matching problem with ties of size two. https://arxiv.org/abs/1808.04510

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