Sparse matrix-sparse matrix multiplication (SpGEMM) is a key kernel in many scientific applications and graph workloads. Unfortunately, SpGEMM is bottlenecked by data movement due to its irregular memory access patterns. Significant work has been devoted to developing row reordering schemes towards improving locality in sparse operations, but prior studies mostly focus on the case of sparse-matrix vector multiplication (SpMV). In this paper, we address these issues with hierarchical clustering for SpGEMM that leverages both row reordering and cluster-wise computation to improve reuse in the second input (B) matrix with a novel row-clustered matrix format and access pattern in the first input (A) matrix. We find that hierarchical clustering can speed up SpGEMM by 1.39x on average with low preprocessing cost (less than 20x the cost of a single SpGEMM on about 90% of inputs). Furthermore, we decouple the reordering algorithm from the clustered matrix format so they can be applied as independent optimizations. Additionally, this paper sheds light on the role of both row reordering and clustering independently and together for SpGEMM with a comprehensive empirical study of the effect of 10 different reordering algorithms and 3 clustering schemes on SpGEMM performance on a suite of 110 matrices. We find that reordering based on graph partitioning provides better SpGEMM performance than existing alternatives at the cost of high preprocessing time. The evaluation demonstrates that the proposed hierarchical clustering method achieves greater average speedup compared to other reordering schemes with similar preprocessing times.

Accepted to appear in the International Conference for High Performance Computing, Networking, Storage, and Analysis (SC) 2025