Efficient Generation of Mandelbrot Set using Message Passing Interface

TL;DR

This paper presents an efficient parallel method for generating the Mandelbrot Set using MPI, comparing three partition schemes and analyzing their performance based on Amdahl's Law and empirical results.

Contribution

It introduces a comparative analysis of three data partition schemes for Mandelbrot Set generation using MPI, highlighting their performance differences under various task counts.

Findings

Alternating Row Segmentation performs better with fewer than 16 tasks.

First Come First Served Row Segmentation outperforms with 16 or more tasks.

Naive Row Segmentation underperforms compared to other schemes.

Abstract

With the increasing need for safer and reliable systems, Mandelbrot Set's use in the encryption world is evident to everyone. This document aims to provide an efficient method to generate this set using data parallelism. First Bernstein's conditions are used to ensure that the Data is parallelizable when generating the Mandelbrot Set. Then Amdhal's Law is used to calculate the theoretical speed up, to be used to compare three partition schemes. The three partition schemes discussed in this document are the Na\"ive Row Segmentation, the First Come First Served Row Segmentation and the Alternating Row Segmentation. The Message Parsing Interface (MPI) library in C is used for all of the communication. After testing all the implementation on MonARCH, the results demonstrate that the Na\"ive Row Segmentation approach did not perform as par. But the Alternating Row Segmentation approach performs better when the number of tasks are $< 16$, where as the First Come First Served approach performs better when the number of tasks is $\ge 16$.