### Abstract

Given a constraint satisfaction problem (CSP) on n variables, x1; x2; : : : ; xn 2 ( ±1), andmconstraints, a global cardinality constraint has the form of Pn i=1 xi = (1 2p)n, where p ∈ ((1); 1 (1)) and pn is an integer. Let AV G be the expected number of constraints satisfied by randomly choosing an assignment to x1; x2; : : : ; xn, complying with the global cardinality constraint. The CSP above average with the global cardinality constraint problem asks whether there is an assignment (complying with the cardinality constraint) that satisfies more than (AV G + t) constraints, where t is an input parameter. In this paper, we present an algorithm that finds a valid assignment satisfying more than (AV G + t) constraints (if there exists one) in time (2O(t2) + nO(d)). Therefore, the CSP above average with the global cardinality constraint problem is fixed-parameter tractable.

Original language | English (US) |
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Title of host publication | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 |

Editors | Philip N. Klein |

Publisher | Association for Computing Machinery, |

Pages | 358-377 |

Number of pages | 20 |

ISBN (Electronic) | 9781611974782 |

DOIs | |

State | Published - Jan 1 2017 |

Externally published | Yes |

Event | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain Duration: Jan 16 2017 → Jan 19 2017 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 |
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Country | Spain |

City | Barcelona |

Period | 1/16/17 → 1/19/17 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017*(pp. 358-377). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery,. https://doi.org/10.1137/1.9781611974782.23