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.

Multi-GPU nodes are increasingly common in the rapidly evolving landscape of exascale supercomputers. On these systems, GPUs on the same node are connected through dedicated networks, with bandwidths up to a few terabits per second. However, gauging performance expectations and maximizing system efficiency is challenging due to different technologies, design options, and software layers. This paper comprehensively characterizes three supercomputers — Alps, Leonardo, and LUMI — each with a unique architecture and design. We focus on performance evaluation of intra-node and inter-node interconnects on up to 4,096 GPUs, using a mix of intra-node and inter-node benchmarks. By analyzing its limitations and opportunities, we aim to offer practical guidance to researchers, system architects, and software developers dealing with multi-GPU supercomputing. Our results show that there is untapped bandwidth, and there are still many opportunities for optimization, ranging from network to software optimization.