Engineering a Distributed-Memory Triangle Counting Algorithm

TL;DR

This paper presents a scalable distributed-memory algorithm for triangle counting in large graphs, significantly reducing communication overhead and enabling efficient processing on thousands of cores.

Contribution

The authors introduce a novel asynchronous sparse-all-to-all operation and indirect routing to improve scalability and speed in distributed triangle counting algorithms.

Findings

Scales up to 32,768 cores

Achieves up to 18x speedup over previous methods

Reduces communication and startup overheads

Abstract

Counting triangles in a graph and incident to each vertex is a fundamental and frequently considered task of graph analysis. We consider how to efficiently do this for huge graphs using massively parallel distributed-memory machines. Unsurprisingly, the main issue is to reduce communication between processors. We achieve this by counting locally whenever possible and reducing the amount of information that needs to be sent in order to handle (possible) nonlocal triangles. We also achieve linear memory requirements despite superlinear communication volume by introducing a new asynchronous sparse-all-to-all operation. Furthermore, we dramatically reduce startup overheads by allowing this communication to use indirect routing. Our algorithms scale (at least) up to 32 768 cores and are up to 18 times faster than the previous state of the art.