Spatiotemporal Graph and Hypergraph Partitioning Models for Sparse Matrix-Vector Multiplication on Many-Core Architectures
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 loca...
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Published in | IEEE transactions on parallel and distributed systems Vol. 30; no. 2; pp. 445 - 458 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
IEEE
01.02.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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Abstract | 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. |
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AbstractList | 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. |
Author | Akbudak, Kadir Aykanat, Cevdet Abubaker, Nabil |
Author_xml | – sequence: 1 givenname: Nabil orcidid: 0000-0002-5060-3059 surname: Abubaker fullname: Abubaker, Nabil email: nabil.abubaker@bilkent.edu.tr organization: Department of Computer Engineering, Bilkent University, Ankara, Turkey – sequence: 2 givenname: Kadir orcidid: 0000-0002-1057-1590 surname: Akbudak fullname: Akbudak, Kadir email: kadir.akbudak@kaust.edu.sa organization: Department of Applied Mathematics and Computational Science, Extreme Computing Research Center, King Abdullah University of Science and Technology, KSA, Thuwal, Saudi Arabia – sequence: 3 givenname: Cevdet orcidid: 0000-0002-4559-1321 surname: Aykanat fullname: Aykanat, Cevdet email: aykanat@cs.bilkent.edu.tr organization: Department of Computer Engineering, Bilkent University, Ankara, Turkey |
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SubjectTerms | 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 |
Title | Spatiotemporal Graph and Hypergraph Partitioning Models for Sparse Matrix-Vector Multiplication on Many-Core Architectures |
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