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+ϵ and 1/2+ϵ.
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-m
approximation-resistant OCSPs accepting only a fraction 1/(m/2)! of
assignments. These results provide the first examples of
approximation-resistant OCSPs subject only to P = \NP