### Abstract

When computing Grobner bases, the efficiency of computation is dominated by the total number of S-polynomials. To decrease the total number of S-polynomials, it is necessary to apply a selection strategy that selects the minimum polynomial as a new element of an intermediate base. A manager worker model is considered. To implement the selection strategy in this parallel model, synchronization between worker processes is required for every selection of a new element of the intermediate base. However, in spite of synchronization, introducing the selection strategy produces not only a better absolute computations speed but also better speedup with multi processors. About 8 times speedup with 64 processors for large problems, T-6 and Ex-17 have been achieved.

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

Pages (from-to) | 201-216 |

Number of pages | 16 |

Journal | Kikai Gijutsu Kenkyusho Shoho/Journal of Mechanical Engineering Laboratory |

Volume | 49 |

Issue number | 5 |

Publication status | Published - 1995 Sep |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Kikai Gijutsu Kenkyusho Shoho/Journal of Mechanical Engineering Laboratory*,

*49*(5), 201-216.

**Parallel computation of Grobner bases on distributed memory machines.** / Sawada, Hiroyuki; Terasaki, Satoshi; Aiba, Akira.

Research output: Contribution to journal › Article

*Kikai Gijutsu Kenkyusho Shoho/Journal of Mechanical Engineering Laboratory*, vol. 49, no. 5, pp. 201-216.

}

TY - JOUR

T1 - Parallel computation of Grobner bases on distributed memory machines

AU - Sawada, Hiroyuki

AU - Terasaki, Satoshi

AU - Aiba, Akira

PY - 1995/9

Y1 - 1995/9

N2 - When computing Grobner bases, the efficiency of computation is dominated by the total number of S-polynomials. To decrease the total number of S-polynomials, it is necessary to apply a selection strategy that selects the minimum polynomial as a new element of an intermediate base. A manager worker model is considered. To implement the selection strategy in this parallel model, synchronization between worker processes is required for every selection of a new element of the intermediate base. However, in spite of synchronization, introducing the selection strategy produces not only a better absolute computations speed but also better speedup with multi processors. About 8 times speedup with 64 processors for large problems, T-6 and Ex-17 have been achieved.

AB - When computing Grobner bases, the efficiency of computation is dominated by the total number of S-polynomials. To decrease the total number of S-polynomials, it is necessary to apply a selection strategy that selects the minimum polynomial as a new element of an intermediate base. A manager worker model is considered. To implement the selection strategy in this parallel model, synchronization between worker processes is required for every selection of a new element of the intermediate base. However, in spite of synchronization, introducing the selection strategy produces not only a better absolute computations speed but also better speedup with multi processors. About 8 times speedup with 64 processors for large problems, T-6 and Ex-17 have been achieved.

UR - http://www.scopus.com/inward/record.url?scp=0029371470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029371470&partnerID=8YFLogxK

M3 - Article

VL - 49

SP - 201

EP - 216

JO - Kikai Gijutsu Kenkyusho Shoho/Journal of Mechanical Engineering Laboratory

JF - Kikai Gijutsu Kenkyusho Shoho/Journal of Mechanical Engineering Laboratory

SN - 0388-4252

IS - 5

ER -