Parallelization of Sparse Matrix Kernels for big data applications

Abstract

Analysis of big data on large-scale distributed systems often necessitates efficient parallel graph algorithms that are used to explore the relationships between individual components. Graph algorithms use the basic adjacency list representation for graphs, which can also be viewed as a sparse matrix. This correspondence between representation of graphs and sparse matrices makes it possible to express many important graph algorithms in terms of basic sparse matrix operations, where the literature for optimization is more mature. For example, the graph analytic libraries such as Pegasus and Combinatorial BLAS use sparse matrix kernels for a wide variety of operations on graphs. In this work, we focus on two such important sparse matrix kernels: Sparse matrix–sparse matrix multiplication (SpGEMM) and sparse matrix–dense matrix multiplication (SpMM). We propose partitioning models for efficient parallelization of these kernels on large-scale distributed systems. Our models aim at reducing and improving communication volume while balancing computational load, which are two vital performance metrics on distributed systems. We show that by exploiting sparsity patterns of the matrices through our models, the parallel performance of SpGEMM and SpMM operations can be significantly improved.