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**An optimal k-consistency algorithm.**
*(English)*
Zbl 0678.68058

Summary: We generalize the arc-consistency algorithm of R. Mohr and T. C. Henderson [Artif. Intell. 28, 225-233 (1986)] and the path- consistency algorithm of C. C. Han and C.-H. Lee [Artif. Intell. 36, 125-130 (1988)] to a k-consistency algorithm (arc-consistency and path-consistency being 2-consistency and 3-consistency, respectively). The algorithm is a development of E. C. Freuder’s synthesis algorithm [Commun. ACM 21, 958-966 (1978; Zbl 0386.68065)]. It simultaneously establishes i-consistency for each \(1\leq i\leq k\). It has worst-case time and space complexity which is optimal when k is a constant and almost optimal for all other values of k. In the case that all order-i constraints exist for all \(1\leq i\leq n\), this algorithm is a solution to the consistent labeling problem with almost optimal worst- case time and space complexity.

### MSC:

68R10 | Graph theory (including graph drawing) in computer science |

68Q25 | Analysis of algorithms and problem complexity |

68W99 | Algorithms in computer science |

### Keywords:

k-consistency algorithm; arc-consistency algorithm; path-consistency algorithm; consistent labeling problem### Citations:

Zbl 0386.68065
Full Text:
DOI

### References:

[1] | Freuder, E.C., Synthesizing constraint expressions, Commun. ACM, 21, 958-966, (1978) · Zbl 0386.68065 |

[2] | Han, C.-C.; Lee, C.-H., Comments on mohr and Henderson’s path consistency algorithm, Artificial intelligence, 36, 125-130, (1988) · Zbl 0709.68534 |

[3] | Mackworth, A.K., Consistency in networks of relations, Artificial intelligence, 8, 99-118, (1977) · Zbl 0341.68061 |

[4] | Mohr, R.; Henderson, T.C., Arc and path consistency revisited, Artificial intelligence, 28, 225-233, (1986) |

[5] | Montanari, U., Networks of constraints: fundamental properties and applications to picture processing, Inform. sci., 7, 95-132, (1974) · Zbl 0284.68074 |

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