English

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

Computer Science and Game Theory 2019-02-19 v2 Optimization and Control

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)