Exploiting Locality in Sparse Matrix-Matrix Multiplication on Many-Core Architectures

• Published in: IEEE transactions on parallel and distributed systems Vol. 28; no. 8; pp. 2258 - 2271
• Main Authors: Akbudak, Kadir, Aykanat, Cevdet
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bipartite graph; bipartite graph model; Central processing units; computational hypergraph model; Computational modeling; Computer architecture; CPUs; Data locality; Data models; graph clustering; graph model; graph partitioning; hypergraph clustering; hypergraph partitioning; Instruction sets; Intel Xeon Phi; many-core architecture; Matrices (mathematics); Microprocessors; Multiplication; Parallel processing; Reuse; Similarity; Sparse matrices; sparse matrix; sparse matrix-matrix multiplication; Sparsity; SpGEMM
• ISSN: 1045-9219; 1558-2183
• DOI: 10.1109/TPDS.2017.2656893

Exploiting spatial and temporal localities is investigated for efficient row-by-row parallelization of general sparse matrix-matrix multiplication (SpGEMM) operation of the form C=AB on many-core architectures. Hypergraph and bipartite graph models are proposed for 1D rowwise partitioning of matrix A to evenly partition the work across threads with the objective of reducing the number of B-matrix words to be transferred from the memory and between different caches. A hypergraph model is proposed for B-matrix column reordering to exploit spatial locality in accessing entries of thread-private temporary arrays, which are used to accumulate results for C-matrix rows. A similarity graph model is proposed for B-matrix row reordering to increase temporal reuse of these accumulation array entries. The proposed models and methods are tested on a wide range of sparse matrices from real applications and the experiments were carried on a 60-core Intel Xeon Phi processor, as well as a two-socket Xeon processor. Results show the validity of the models and methods proposed for enhancing the locality in parallel SpGEMM operations.