### Abstract

We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We prove the conjecture of Gutin, van Iersel, Mnich, and Yeo that the satisfiability above average of ordering CSPs of arity k is fixed-parameter tractable for every k. Previously, this was only known for k=2 and k=3. We also generalize this result to more general classes of CSPs, including CSPs with predicates defined by linear equations. To obtain our results, we prove a new Bonami-type inequality for the Efron - Stein decomposition. The inequality applies to functions defined on arbitrary product probability spaces. In contrast to other variants of the Bonami Inequality, it does not depend on the mass of the smallest atom in the probability space. We believe that this inequality is of independent interest.

Original language | English (US) |
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Title of host publication | Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015 |

Publisher | IEEE Computer Society |

Pages | 975-993 |

Number of pages | 19 |

ISBN (Electronic) | 9781467381918 |

DOIs | |

State | Published - Dec 11 2015 |

Externally published | Yes |

Event | 56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015 - Berkeley, United States Duration: Oct 17 2015 → Oct 20 2015 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 2015-December |

ISSN (Print) | 0272-5428 |

### Other

Other | 56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015 |
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Country | United States |

City | Berkeley |

Period | 10/17/15 → 10/20/15 |

### Fingerprint

### Keywords

- advantage over random
- combinatorial optimization
- fixed-parameter tractability
- ordering CSP

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015*(pp. 975-993). [7354438] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2015-December). IEEE Computer Society. https://doi.org/10.1109/FOCS.2015.64

**Satisfiability of Ordering CSPs above Average is Fixed-Parameter Tractable.** / Makarychev, Konstantin; Makarychev, Yury; Zhou, Yuan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015.*, 7354438, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 2015-December, IEEE Computer Society, pp. 975-993, 56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015, Berkeley, United States, 10/17/15. https://doi.org/10.1109/FOCS.2015.64

}

TY - GEN

T1 - Satisfiability of Ordering CSPs above Average is Fixed-Parameter Tractable

AU - Makarychev, Konstantin

AU - Makarychev, Yury

AU - Zhou, Yuan

PY - 2015/12/11

Y1 - 2015/12/11

N2 - We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We prove the conjecture of Gutin, van Iersel, Mnich, and Yeo that the satisfiability above average of ordering CSPs of arity k is fixed-parameter tractable for every k. Previously, this was only known for k=2 and k=3. We also generalize this result to more general classes of CSPs, including CSPs with predicates defined by linear equations. To obtain our results, we prove a new Bonami-type inequality for the Efron - Stein decomposition. The inequality applies to functions defined on arbitrary product probability spaces. In contrast to other variants of the Bonami Inequality, it does not depend on the mass of the smallest atom in the probability space. We believe that this inequality is of independent interest.

AB - We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We prove the conjecture of Gutin, van Iersel, Mnich, and Yeo that the satisfiability above average of ordering CSPs of arity k is fixed-parameter tractable for every k. Previously, this was only known for k=2 and k=3. We also generalize this result to more general classes of CSPs, including CSPs with predicates defined by linear equations. To obtain our results, we prove a new Bonami-type inequality for the Efron - Stein decomposition. The inequality applies to functions defined on arbitrary product probability spaces. In contrast to other variants of the Bonami Inequality, it does not depend on the mass of the smallest atom in the probability space. We believe that this inequality is of independent interest.

KW - advantage over random

KW - combinatorial optimization

KW - fixed-parameter tractability

KW - ordering CSP

UR - http://www.scopus.com/inward/record.url?scp=84960358298&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960358298&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2015.64

DO - 10.1109/FOCS.2015.64

M3 - Conference contribution

AN - SCOPUS:84960358298

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 975

EP - 993

BT - Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015

PB - IEEE Computer Society

ER -