A Note on Parallel Algorithmic Speedup Bounds

TL;DR

This paper explores the relationship between critical path execution time, Amdahl speedup, and average parallelism in parallel algorithms, establishing bounds that exclude superlinear speedup.

Contribution

It formally connects critical path performance bounds with Amdahl speedup and average parallelism, clarifying limitations of superlinear speedup in parallel algorithms.

Findings

Critical path bounds relate to Amdahl speedup.

Superlinear speedup is formally excluded.

Provides a framework for analyzing parallel algorithm performance.

Abstract

A parallel program can be represented as a directed acyclic graph. An important performance bound is the time to execute the critical path through the graph. We show how this performance metric is related to Amdahl speedup and the degree of average parallelism. These bounds formally exclude superlinear performance.