Communication-Avoiding SpGEMM via Trident Partitioning on Hierarchical GPU Interconnects

TL;DR

This paper introduces Trident, a hierarchy-aware 2D distributed SpGEMM algorithm that reduces communication and improves performance on hierarchical GPU interconnects by exploiting intra-node bandwidth advantages.

Contribution

The paper presents a novel trident partitioning scheme and communication-avoiding techniques tailored for hierarchical GPU architectures, significantly enhancing sparse matrix multiplication efficiency.

Findings

Up to 2.38x speedup over traditional 2D SpGEMM

Internode communication volume reduced by up to 2x

Effective acceleration of Markov Clustering tasks

Abstract

The multiplication of two sparse matrices, known as SpGEMM, is a key kernel in scientific computing and large-scale data analytics, underpinning graph algorithms, machine learning, simulations, and computational biology, where sparsity is often highly unstructured. The unstructured sparsity makes achieving high performance challenging because it limits both memory efficiency and scalability. In distributed memory, the cost of exchanging and merging partial products across nodes further constrains performance. These issues are exacerbated on modern heterogeneous supercomputers with deep, hierarchical GPU interconnects. Current SpGEMM implementations overlook the gap between intra-node and inter-node bandwidth, resulting in unnecessary data movement and synchronization not fully exploiting the fast intra-node interconnect. To address these challenges, we introduce Trident, a hierarchy-aware 2D distributed SpGEMM algorithm that uses communication-avoiding techniques and asynchronous communication to exploit the hierarchical and heterogeneous architecture of modern supercomputing interconnect. Central to Trident is the novel trident partitioning scheme, which enables hierarchy-aware decomposition and reduces internode communication by leveraging the higher bandwidth between GPUs within a node compared to across nodes. Here, we evaluate Trident on unstructured matrices, achieving up to $2.38\times$ speedup over a 2D SpGEMM with a corresponding geometric mean speedup of $1.54\times$. Trident reduces internode communication volume by up to $2\times$ on NERSC's Perlmutter supercomputer. Furthermore, we demonstrate the effectiveness of Trident in speeding up Markov Clustering, achieving up to $2\times$ speedup compared to competing strategies.