On the NP-hardness of approximating ordering-constraint satisfaction problems

We show improved NPNP-hardness of approximating Ordering-Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove NPNP-hard approximation factors of 14/15+ε14/15+ε and 1/2+ε1/2+ε. When it is hard to approximate an OCSP...

Full description

Saved in:
Bibliographic Details
Published inTheory of computing (Chicago, Ill.) Vol. 11; p. 257
Main Authors Austrin, Per, Manokaran, Rajsekar, Wenner, Cenny
Format Journal Article
LanguageEnglish
Published 2015
Subjects
Acyclic subgraph
APPROX
Approximation
Approximation resistance
Betweenness
Computer Science
Constraint satisfaction
Constraint satisfaction problems
CSPs
datalogi
Feedback arc set
Feedback arc sets
Hardness
Hypercontractivity
NP-completeness
NP-hard
Orderings
PCP
Probabilistically checkable proof
Probabilistically checkable proofs
Online AccessGet full text

Cover

More Information
Summary:We show improved NPNP-hardness of approximating Ordering-Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove NPNP-hard approximation factors of 14/15+ε14/15+ε and 1/2+ε1/2+ε. When it is hard to approximate an OCSP by a constant better than taking a uniformly-at-random ordering, then the OCSP is said to be approximation resistant. We show 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)! of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P≠NP.
ISSN:1557-2862
1557-2862
DOI:10.4086/toc.2015.v011a010