English

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

Computational Complexity 2013-07-22 v1

Abstract

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of 14/15+ϵ14/15+\epsilon and 1/2+ϵ1/2+\epsilon. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-mm approximation-resistant OCSPs accepting only a fraction 1/(m/2)!1 / (m/2)! of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P \neq \NP.

Keywords

Cite

@article{arxiv.1307.5090,
  title  = {On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems},
  author = {Per Austrin and Rajsekar Manokaran and Cenny Wenner},
  journal= {arXiv preprint arXiv:1307.5090},
  year   = {2013}
}
R2 v1 2026-06-22T00:54:03.840Z