The actual complexity of parallel evaluation of low degree polynomials

doi:10.1016/0167-8191(90)90120-X

Parallel Computing

Volume 13, Issue 1, January 1990, Pages 73-83

https://doi.org/10.1016/0167-8191(90)90120-X Get rights and content

Abstract

We consider several sequential and parallel algorithms for the evaluation of polynomials of low degree, with particular emphasis on those that are used frequently in computer graphics. A complete accounting of computation times for the speedup and efficiency of these algorithms is reported. The results are compared to standard estimates of these quantities for single and multi-processors using classical complexity theory. A simulator which is configurable to several parallel architectures is used to provide validation of the results obtained.

References (10)

V Faber et al.
Comments on the paper “Parallel efficiency can be greater than unity”
Parallel Comput.
(1987)
R Janβen
A note on superlinear speedup
Parallel Comput.
(1987)
I Munro et al.
Optimal algorithms for parallel polynomial evaluation
J. Comput. System Sci.
(1973)
D Parkinson
Parallel efficiency can be greater than unity
Parallel Comput.
(1986)
W.S Dorn
Generalizations of Horner's rule for polynomial evaluation
IBM J. Res. Develop.
(1962)

There are more references available in the full text version of this article.

Cited by (3)

Data-movement-intensive problems: two folk theorems in parallel computation revisited
1992, Theoretical Computer Science
Two “folk theorems” that permeate the parallel computation literature are reconsidered in this paper. The first of these, known as the speedup theorem, states that the maximum speedup a sequential computation can undergo when p processors are used is p. The second theorem, known as Brent's theorem, states that a computation requiring one step and n processors can be executed by p processors in at most ⌈n/p⌉ steps. We show that these two theorems are not true in general. Specifically, we exhibit for each theorem a problem to which the theorem does not apply. Both problems belong to a class of problems that we term “data-movement-intensive”. Problems in this class are inherently parallel and, as a consequence, appear to be inefficient to solve sequentially or when the number of processors used is less than the maximum possible. Our approach is purely theoretical and uses only abstract models of computation, namely, the RAM and PRAM. Practical issues pertaining to the applicability of our results to specific existing computers, whether sequential or parallel, are not addressed.
Parallel synergy
1993, Parallel Algorithms and Applications
Revisiting parallel speedup complexity
1992, Proceedings - ICCI 1992: 4th International Conference on Computing and Information

View full text

The actual complexity of parallel evaluation of low degree polynomials

Abstract

Parallel Comput.

Parallel Comput.

J. Comput. System Sci.

Parallel Comput.

Generalizations of Horner's rule for polynomial evaluation

IBM J. Res. Develop.