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 |
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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 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Information Systems
- Hardware and Architecture
- Computational Theory and Mathematics