On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

  • Per Austrin
  • Rajsekar Manokaran
  • Cenny Wenner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8096)

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 PNP.

Our reductions from Label Cover differ from previous works in two ways. First, we establish a somewhat general bucketing lemma permitting us to reduce the analysis of ordering predicates to that of classical predicates. Second, instead of “folding”, which is not available for ordering predicates, we employ permuted instantiations of the predicates to limit the value of poorly correlated strategies.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Per Austrin
    • 1
  • Rajsekar Manokaran
    • 1
  • Cenny Wenner
    • 1
  1. 1.School of Computer Science and CommunicationKTH – Royal Institute of TechnologyStockholmSweden

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