### Abstract

We introduce a concept of local computability for designing high‐speed parallel algorithms on fan‐in restricted models. A function is k‐locally computable if each subfunction sepends on only at most k input variables. If k is a constant independent of n, the number of input variables, we can construct an O(1) time parallel algorithm for F on a fan‐in restricted computation model. In order to realize the local computability, we use a redundant coding scheme. We show that a binary operation of any finite Abelian group is k‐locally computable under a redundant coding scheme, where k is a constant independent of the order of the group. We also show that we can design a redundant coding scheme for a residue ring Z_{m} of integers under which addition and multiplication can be performed in O(1) and O(log log log m) time, respectively, in parallel, when m is the product of the smallest r primes.

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

Pages (from-to) | 72-80 |

Number of pages | 9 |

Journal | Systems and Computers in Japan |

Volume | 18 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1987 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*Systems and Computers in Japan*,

*18*(12), 72-80. https://doi.org/10.1002/scj.4690181208

**On high‐speed parallel algorithms using redundant coding.** / Yasuura, Hiroto; Takagi, Naofumi; Yajima, Shuzo.

Research output: Contribution to journal › Article

*Systems and Computers in Japan*, vol. 18, no. 12, pp. 72-80. https://doi.org/10.1002/scj.4690181208

}

TY - JOUR

T1 - On high‐speed parallel algorithms using redundant coding

AU - Yasuura, Hiroto

AU - Takagi, Naofumi

AU - Yajima, Shuzo

PY - 1987

Y1 - 1987

N2 - We introduce a concept of local computability for designing high‐speed parallel algorithms on fan‐in restricted models. A function is k‐locally computable if each subfunction sepends on only at most k input variables. If k is a constant independent of n, the number of input variables, we can construct an O(1) time parallel algorithm for F on a fan‐in restricted computation model. In order to realize the local computability, we use a redundant coding scheme. We show that a binary operation of any finite Abelian group is k‐locally computable under a redundant coding scheme, where k is a constant independent of the order of the group. We also show that we can design a redundant coding scheme for a residue ring Zm of integers under which addition and multiplication can be performed in O(1) and O(log log log m) time, respectively, in parallel, when m is the product of the smallest r primes.

AB - We introduce a concept of local computability for designing high‐speed parallel algorithms on fan‐in restricted models. A function is k‐locally computable if each subfunction sepends on only at most k input variables. If k is a constant independent of n, the number of input variables, we can construct an O(1) time parallel algorithm for F on a fan‐in restricted computation model. In order to realize the local computability, we use a redundant coding scheme. We show that a binary operation of any finite Abelian group is k‐locally computable under a redundant coding scheme, where k is a constant independent of the order of the group. We also show that we can design a redundant coding scheme for a residue ring Zm of integers under which addition and multiplication can be performed in O(1) and O(log log log m) time, respectively, in parallel, when m is the product of the smallest r primes.

UR - http://www.scopus.com/inward/record.url?scp=0023589675&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023589675&partnerID=8YFLogxK

U2 - 10.1002/scj.4690181208

DO - 10.1002/scj.4690181208

M3 - Article

AN - SCOPUS:0023589675

VL - 18

SP - 72

EP - 80

JO - Systems and Computers in Japan

JF - Systems and Computers in Japan

SN - 0882-1666

IS - 12

ER -