### Abstract

We observe a repeated-update problem in the process of updating walkabout strengths of the DeltaBlue algorithm, which is known as a fast constraint solving method based on local propagation. According to the basic references on the DeltaBlue algorithm, the time complexity of the planning phase is described as O(MN) for a constraint problem such that the number of constraints is N and the maximum number of methods a constraint has is M. We, however, point out that the time complexity is not O(MN) using a very simple example. In this example, the time complexity is exponential order for N. Then we present a corrected DeltaBlue algorithm whose time complexity is O(EN^{2}) for a constraint problem such that the number of constraints is N and the maximum number of variables a constraint has is E. Finally we measure the performance of the corrected DeltaBlue algorithm using two benchmarks.

Original language | English |
---|---|

Pages (from-to) | 331-341 |

Number of pages | 11 |

Journal | Constraints |

Volume | 3 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1998 Oct |

Externally published | Yes |

### Fingerprint

### Keywords

- Constraint solving algorithm
- DeltaBlue algorithm
- Local propagation

### ASJC Scopus subject areas

- Hardware and Architecture
- Applied Mathematics

### Cite this

*Constraints*,

*3*(4), 331-341. https://doi.org/10.1023/A:1009776022504

**A repeated-update problem in the DeltaBlue algorithm.** / Suzuki, Tetsuya; Tokuda, Takehiro.

Research output: Contribution to journal › Article

*Constraints*, vol. 3, no. 4, pp. 331-341. https://doi.org/10.1023/A:1009776022504

}

TY - JOUR

T1 - A repeated-update problem in the DeltaBlue algorithm

AU - Suzuki, Tetsuya

AU - Tokuda, Takehiro

PY - 1998/10

Y1 - 1998/10

N2 - We observe a repeated-update problem in the process of updating walkabout strengths of the DeltaBlue algorithm, which is known as a fast constraint solving method based on local propagation. According to the basic references on the DeltaBlue algorithm, the time complexity of the planning phase is described as O(MN) for a constraint problem such that the number of constraints is N and the maximum number of methods a constraint has is M. We, however, point out that the time complexity is not O(MN) using a very simple example. In this example, the time complexity is exponential order for N. Then we present a corrected DeltaBlue algorithm whose time complexity is O(EN2) for a constraint problem such that the number of constraints is N and the maximum number of variables a constraint has is E. Finally we measure the performance of the corrected DeltaBlue algorithm using two benchmarks.

AB - We observe a repeated-update problem in the process of updating walkabout strengths of the DeltaBlue algorithm, which is known as a fast constraint solving method based on local propagation. According to the basic references on the DeltaBlue algorithm, the time complexity of the planning phase is described as O(MN) for a constraint problem such that the number of constraints is N and the maximum number of methods a constraint has is M. We, however, point out that the time complexity is not O(MN) using a very simple example. In this example, the time complexity is exponential order for N. Then we present a corrected DeltaBlue algorithm whose time complexity is O(EN2) for a constraint problem such that the number of constraints is N and the maximum number of variables a constraint has is E. Finally we measure the performance of the corrected DeltaBlue algorithm using two benchmarks.

KW - Constraint solving algorithm

KW - DeltaBlue algorithm

KW - Local propagation

UR - http://www.scopus.com/inward/record.url?scp=10044269965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10044269965&partnerID=8YFLogxK

U2 - 10.1023/A:1009776022504

DO - 10.1023/A:1009776022504

M3 - Article

VL - 3

SP - 331

EP - 341

JO - Constraints

JF - Constraints

SN - 1383-7133

IS - 4

ER -