On the Algebraic Properties of Flame Graphs

TL;DR

This paper introduces a mathematical framework for flame graphs, revealing algebraic properties and enabling advanced analysis techniques to utilize full profiling data for performance regression.

Contribution

It provides a formal mathematical definition of flame graphs, unlocking algebraic properties and new operations for comprehensive performance analysis.

Findings

Algebraic properties of flame graphs are identified.

New operations enable in-depth performance regression analysis.

Combining mathematical and statistical methods enhances data utilization.

Abstract

Flame graphs are a popular way of representing profiling data. In this paper we propose a possible mathematical definition of flame graphs. In doing so, we gain some interesting algebraic properties almost for free, which in turn allow us to define some operations that can allow to perform an in-depth performance regression analysis. The typical documented use of a flame graph is via its graphical representation, whereby one scans the picture for the largest plateaux. Whilst this method is effective at finding the main sources of performance issues, it leaves quite a large amount of data potentially unused. By combining a mathematical precise definition of flame graphs with some statistical methods we show how to generalise this visual procedure and make the best of the full set of collected profiling data.