Arc consistency for factorable relations.

*(English)*Zbl 1193.68140Summary: An optimal arc consistency algorithm AC-4 was given by Mohr and Henderson. AC-4 has cost \(O(ed^2)\), and cost \(O(nd^2)\) for scene labelling. Although their algorithm is indeed optimal, under certain conditions a constraint satisfaction problem can be transformed into a less complex problem. In this paper, we present conditions and mechanisms for such representational transformations, and show how to factor relations into more manageable components. We describe how factorization can reduce AC-4’s cost to \(O(ed)\), and apply this result to RETE match. Further, with our factorization, the cost of scene labelling is reduced to \(O(nd)\).

##### MSC:

68Q25 | Analysis of algorithms and problem complexity |

PDF
BibTeX
XML
Cite

\textit{M. Perlin}, Artif. Intell. 53, No. 2--3, 329--342 (1992; Zbl 1193.68140)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Cooley, J.M.; Tukey, J.W., An algorithm for the machine calculation of complex Fourier series, Math. comp., 19, 297-301, (1965) · Zbl 0127.09002 |

[2] | Deville, Y.; Van Hentenryck, P., Efficient arc consistency algorithm for a class of CSP problems, () |

[3] | Forgy, C.L., Rete: a fast algorithm for the many pattern/many object pattern match problem, Artif. intell., 19, 1, 17-37, (1982) |

[4] | Gupta, A., Parallelism in production systems, () · Zbl 0757.68091 |

[5] | Horowitz, E.; Sahni, S., () |

[6] | Mackworth, A.K., Consistency in networks of relations, Artif. intell., 8, 99-118, (1977) · Zbl 0341.68061 |

[7] | Mackworth, A.K.; Freuder, E.C., The complexity of some polynomial network consistency algorithms for constraint satisfaction problems, Artif. intell., 25, 65-74, (1985) |

[8] | Mohr, R.; Henderson, T.C., Arc and path consistency revisited, Artif. intell., 28, 225-233, (1986) |

[9] | Mohr, R.; Masini, G., Good old discrete relaxation, (), 651-656 |

[10] | Mohr, R.; Masini, G., Running efficiently arc consistency, (), 217-231 |

[11] | Pasik, A, Improving production system performance on parallel architectures by creating constrained copies of culprit rules, () |

[12] | Perlin, M.W., Reducing computation by unifying inference with user interface, () |

[13] | Perlin, M.W., Call-graph caching: transforming programs into networks, (), 122-128 · Zbl 0707.68058 |

[14] | Perlin, M.W., Constraint-based specification of production rules, (), 332-338 |

[15] | Perlin, M.W., Automating the construction of efficient artificial intelligence algorithms, () |

[16] | Perlin, M.W., Transforming conjunctive match into RETE: a call-graph caching approach, Int. J. softw. eng. knowl. eng., (1991) |

[17] | Perlin, M.W., (), © |

[18] | Perlin, M.W.; Debaud, J.-M., Match box: fine-grained parallelism at the match level, (), 428-434 |

[19] | Perlin, M.W.; Gaertner, P., A graphical constraint-based production system environment, () |

[20] | Scales, D.J., Efficient matching algorithms for the soar/ops5 production system, () |

[21] | Waltz, D., Understanding line drawings of scenes with shadows, (), 19-91 |

[22] | () |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.