Towards an Objective Metric for the Performance of Exact Triangle Count

TL;DR

This paper proposes a new objective performance metric for exact triangle counting in graphs, addressing limitations of traditional TEPS metrics, and demonstrates its effectiveness in comparing different algorithmic approaches.

Contribution

The paper introduces a novel performance metric tailored for exact triangle counting, capturing the interaction between work done and hardware capabilities.

Findings

The new metric better correlates with execution times across different hardware.

It effectively differentiates between various triangle counting techniques.

The SIMD approach outperforms the scalar baseline under the new metric.

Abstract

The performance of graph algorithms is often measured in terms of the number of traversed edges per second (TEPS). However, this performance metric is inadequate for a graph operation such as exact triangle counting. In triangle counting, execution times on graphs with a similar number of edges can be distinctly different as demonstrated by results from the past Graph Challenge entries. We discuss the need for an objective performance metric for graph operations and the desired characteristics of such a metric such that it more accurately captures the interactions between the amount of work performed and the capabilities of the hardware on which the code is executed. Using exact triangle counting as an example, we derive a metric that captures how certain techniques employed in many implementations improve performance. We demonstrate that our proposed metric can be used to evaluate and compare multiple approaches for triangle counting, using a SIMD approach as a case study against a scalar baseline.