Regularizing irregularity

Abstract

Graphs can be naturally represented as sparse matrices. The relationship between graph algorithms and linear algebra algorithms is well understood and many graph problems can be abstracted as Sparse General Matrix-Matrix Multiplication (SpGEMM) operations. While quite some matrix storage formats, including bitmap-based ones, have been proposed for sparse matrices, they are mostly evaluated on the simpler Sparse Matrix-Vector Multiplication (SpMV) problems. In this study, we have developed data parallel algorithms to pair up bitmap-indexed sparse matrix blocks for SpGEMM using data parallel primitives for portability. Experiments on the WebBase-1M dataset with more than one million rows and columns and three million non-zero values have shown that our technique on squaring the large-scale sparse matrix using a 2013 GTX Titan GPU can complete in about 300 milliseconds. The runtime is 2.4X faster than CUSP and 3.5X faster than bhSPARSE, the two leading open source SpGEMM packages. Furthermore, our bitmap-indexed sparse matrix blocks can be efficiently converted to regular small dense matrices and subsequently utilize new hardware accelerations, such as tensor cores inside Nvidia Volta GPUs and Google Tensor Processing Units (TPUs), for more efficient implementations.