Spatiotemporal Graph and Hypergraph Partitioning Models for Sparse Matrix-Vector Multiplication on Many-Core Architectures

• Published in: IEEE transactions on parallel and distributed systems Vol. 30; no. 2; pp. 445 - 458
• Main Authors: Abubaker, Nabil, Akbudak, Kadir, Aykanat, Cevdet
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bipartite graph; bipartite graph model; Computer architecture; Computer memory; data locality; Data models; Encoding; graph model; graph partitioning; Graph theory; Graphs; hypergraph model; hypergraph partitioning; Intel many integrated core architecture; Intel Xeon Phi; Mathematical analysis; Matrix algebra; Matrix methods; Microprocessors; Multiplication; Partitioning; Sparse matrices; Sparse matrix; sparse matrix-vector multiplication; Sparsity; spatial locality; Spatiotemporal phenomena; Task analysis; Taxonomy; temporal locality
• ISSN: 1045-9219; 1558-2183
• DOI: 10.1109/TPDS.2018.2864729

There exist graph/hypergraph partitioning-based row/column reordering methods for encoding either spatial or temporal locality for sparse matrix-vector multiplication (SpMV) operations. Spatial and temporal hypergraph models in these methods are extended to encapsulate both spatial and temporal localities based on cut/uncut net categorization obtained from vertex partitioning. These extensions of spatial and temporal hypergraph models encode the spatial locality primarily and the temporal locality secondarily, and vice-versa, respectively. However, the literature lacks models that simultaneously encode both spatial and temporal localities utilizing only vertex partitioning for further improving the performance of SpMV on shared-memory architectures. In order to fill this gap, we propose a novel spatiotemporal hypergraph model that leads to a one-phase spatiotemporal reordering method which encodes both types of locality simultaneously. We also propose a framework for spatiotemporal methods which encodes both types of locality in two dependent phases and two separate phases. The validity of the proposed spatiotemporal models and methods are tested on a wide range of sparse matrices and the experiments are performed on both a 60-core Intel Xeon Phi processor and a Xeon processor. Results show the validity of the methods via almost doubling the Gflop/s performance through enhancing data locality in parallel SpMV operations.