Method for determining the acceleration of a parallel specialised computer system based on Amdahl's law

TL;DR

This paper modifies Amdahl's law to evaluate the maximum theoretical acceleration of parallel specialized computer systems as processor elements increase, providing a new method to predict performance gains for various algorithms.

Contribution

It introduces a modified Amdahl's law-based method to determine the maximum acceleration of parallel systems with increasing processor elements, including theoretical limits and practical testing.

Findings

Coefficient k > 1 for any positive processor increment

Derived formulas for maximum acceleration of parallel systems

Method validated on multiple algorithms

Abstract

The modification of Amdahl's law for the case of increment of processor elements in a computer system is considered. The coefficient $k$ linking accelerations of parallel and parallel specialized computer systems is determined. The limiting values of the coefficient are investigated and its theoretical maximum is calculated. It is proved that $k$ > 1 for any positive increment of processor elements. The obtained formulas are combined into a single method allowing to determine the maximum theoretical acceleration of a parallel specialized computer system in comparison with the acceleration of a minimal parallel computer system. The method is tested on Apriori, k-nearest neighbors, CDF 9/7, fast Fourier transform and naive Bayesian classifier algorithms.