### Abstract

We prove that the Bounded Occurrence Ordering k-CSP Problem is not approximation resistant. We give a very simple local search algorithm that always performs better than the random assignment algorithm (unless, the number of satisfied constraints does not depend on the ordering). Specifically, the expected value of the solution returned by the algorithm is at least Alg ≤ Avg + α(B, k)(Opt - Avg), where Opt is the value of the optimal solution; Avg is the expected value of the random solution; and α (B, k) = k(B-(k+O(1))) is a parameter depending only on k (the arity of the CSP) and B (the maximum number of times each variable is used in constraints). The question whether bounded occurrence ordering k-CSPs are approximation resistant was raised by Hastad [6], who recently showed that bounded occurrence 3-CSPs and monotone k-CSPs admit a non-trivial approximation.

Original language | English (US) |
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Title of host publication | 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013 |

Pages | 139-147 |

Number of pages | 9 |

DOIs | |

State | Published - Dec 1 2013 |

Event | 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013 - Kiel, Germany Duration: Feb 27 2013 → Mar 2 2013 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 20 |

ISSN (Print) | 1868-8969 |

### Other

Other | 30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013 |
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Country | Germany |

City | Kiel |

Period | 2/27/13 → 3/2/13 |

### Keywords

- Approximation algorithms
- Approximation resistance
- Ordering CSPs

### ASJC Scopus subject areas

- Software

## Cite this

*30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013*(pp. 139-147). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 20). https://doi.org/10.4230/LIPIcs.STACS.2013.139