On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

Per Austrin; Rajsekar Manokaran; Cenny Wenner

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arXiv · 1307.5090

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

Per Austrin·Rajsekar Manokaran·Cenny Wenner

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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 $14/15+ε$ 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 $\neq$ \NP.

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BibTeX RIS

Per Austrin, Rajsekar Manokaran, Cenny Wenner. 2013-07-18. On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems. https://arxiv.org/abs/1307.5090

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