### Abstract

The tightness of a constraint refers to how restricted the constraint is. The existing work shows that there exists a relationship between tightness and global consistency of a constraint network. In this paper, we conduct a comprehensive study on this relationship. Under the concept of k-consistency (k is a number), we strengthen the existing results by establishing that only some of the tightest, not all, binary constraints are used to predict a number k such that strong k-consistency ensures global consistency of an arbitrary constraint network which may include non-binary constraints. More importantly, we have identified a lower bound of the number of the tightest constraints we have to consider in predicting the number k. To make better use of the tightness of constraints, we propose a new type of consistency: dually adaptive consistency. Under this concept, only the tightest directionally relevant constraint on each variable (and thus in total n - 1 such constraints where n is the number of variables) will be used to predict the level of "consistency" ensuring global consistency of a network.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Mark Wallace |

Publisher | Springer-Verlag |

Pages | 777-781 |

Number of pages | 5 |

ISBN (Print) | 3540232419, 9783540232414 |

DOIs | |

State | Published - 2004 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3258 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 777-781). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3258). Springer-Verlag. https://doi.org/10.1007/978-3-540-30201-8_65