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

TL;DR

This work extends Amdahl's law to quantify the acceleration gain $k$ when moving from a conventional parallel system to a parallel specialised system with an increment $\Delta P$ in processors, showing $k > 1$ for any $\Delta P > 0$ and deriving $\max(k) = \frac{f+1}{2f}$ where $f$ is the non-parallelizable fraction. It provides a unified method to estimate the maximum theoretical speedup of a specialised system and validates the approach by analyzing five Big Data algorithms (Apriori, KNN, CDF 9/7, FFT, NBC), computing the fraction of parallelizable work and the corresponding $k$ values. The results indicate that wavelet-based CFD 9/7 offers the highest potential acceleration among the studied tasks, illustrating how the method guides hardware specialization decisions. Overall, the paper delivers a practical framework for predicting theoretical speedups and selecting algorithm candidates for specialised parallel hardware in Big Data contexts.

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.

Figures (1)

• Figure 1: Comparison of specialised acceleration coefficients of Big Data algorithms