A Reexamination of the Communication Bandwidth Cost Analysis of A Parallel Recursive Algorithm for Solving Triangular Systems of Linear Equations

TL;DR

This paper critically reexamines the communication bandwidth cost analysis of a parallel recursive algorithm for triangular system solving, identifying issues and clarifying the cost categorization to improve understanding in high-performance computing.

Contribution

It provides a revised analysis of communication costs in parallel recursive algorithms for triangular systems, addressing previous inconsistencies and enhancing theoretical understanding.

Findings

Identified and corrected miscalculations in the original cost analysis

Clarified the categorization of communication costs based on matrix and processor parameters

Contributed to more accurate modeling of communication costs in parallel algorithms

Abstract

This paper presents a reexamination of the research paper titled "Communication-Avoiding Parallel Algorithms for \proc{TRSM}" by Wicky et al. We focus on the communication bandwidth cost analysis presented in the original work and identify potential issues that require clarification or revision. The problem at hand is the need to address inconsistencies and miscalculations found in the analysis, particularly in the categorization of costs into three scenarios based on the relationship between matrix dimensions and processor count. Our findings contribute to the ongoing discourse in the field and pave the way for further improvements in this area of research.