On high‐speed parallel algorithms using redundant coding

Hiroto Yasuura, Naofumi Takagi, Shuzo Yajima

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)72-80
Number of pages9
JournalSystems and Computers in Japan
Volume18
Issue number12
DOIs
Publication statusPublished - 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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