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On the Approximability of the Stable Matching Problem with Ties of Size Two

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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 \(\mathcal{NP}\)-hard problem, even when the ties are of size two. Moreover, in this setting it is UGC-hard to provide an approximation 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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Acknowledgements

We would like to thank Laura Sanità for suggesting to us the maximum cardinality stable matching problem with ties of size two.

Funding

Funded by Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, ON, Canada

    Robert Chiang

  2. School of Computer Science and Electrical Engineering, University of Ottawa, 800 King Edward Avenue, Ottawa, K1N 6N5, ON, Canada

    Kanstantsin Pashkovich

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  1. Robert Chiang
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  2. Kanstantsin Pashkovich
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Correspondence to Kanstantsin Pashkovich.

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Chiang, R., Pashkovich, K. On the Approximability of the Stable Matching Problem with Ties of Size Two. Algorithmica 82, 2668–2686 (2020). https://doi.org/10.1007/s00453-020-00703-9

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  • DOI: https://doi.org/10.1007/s00453-020-00703-9

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