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 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.
| 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
On high‐speed parallel algorithms using redundant coding. / Yasuura, Hiroto; Takagi, Naofumi; Yajima, Shuzo.
In: Systems and Computers in Japan, Vol. 18, No. 12, 1987, p. 72-80.Research output: Contribution to journal › Article
}
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.
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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 -