Parallel GPU-Enabled Algorithms for SpGEMM on Arbitrary Semirings with Hybrid Communication

Sparse General Matrix Multiply (SpGEMM) is key for various High-Performance Computing (HPC) applications such as genomics and graph analytics. Using the semiring abstraction, many algorithms can be formulated as SpGEMM, allowing redefinition of addition, multiplication, and numeric types. Today large input matrices require distributed memory parallelism to avoid disk I/O, and modern HPC machines with GPUs can greatly accelerate linear algebra computation. In this paper, we implement a GPU-based distributed-memory SpGEMM routine on top of the CombBLAS library. Our implementation achieves a speedup of over 2x compared to the CPU-only CombBLAS implementation and up to 3x compared to PETSc for large input matrices. Furthermore, we note that communication between processes can be optimized by either direct host-to-host or device-to-device communication, depending on the message size. To exploit this, we introduce a hybrid communication scheme that dynamically switches data paths depending on the message size, thus improving runtimes in communication-bound scenarios.