On the approximability of the stable matching problem with ties of size two
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.
Keywords
Cite
@article{arxiv.1808.04510,
title = {On the approximability of the stable matching problem with ties of size two},
author = {Robert Chiang and Kanstantsin Pashkovich},
journal= {arXiv preprint arXiv:1808.04510},
year = {2019}
}
Comments
Added a detailed comparison with the approaches from the papers "On the approximability of the stable marriage problem with one-sided ties." by Bauckholt, Pashkovich, and Sanita and "Improved approximation algorithms for two variants of the stable marriage problem with ties." by Huang and Kavitha. (See Appendix)