带大小为二的平局的稳定匹配问题的可近似性
计算机科学与博弈论
2019-02-19 v2 最优化与控制
摘要
稳定匹配问题是算法博弈论的核心问题之一。若允许参与者有平局，则寻找最大基数稳定匹配的问题是NP难问题，即使平局大小为二。此外，在此设定下，对最大基数稳定匹配问题提供小于4/3常数因子的近似是UGC难的。本文对Huang和Kavitha所给出的针对带大小为二的平局的最大基数稳定匹配问题的近似算法给出紧分析，证明其近似因子改进为4/3。
引用
@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}
}
备注
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)