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      Hypergraph partitioning based models and methods for exploiting cache locality in sparse matrix-vector multiplication

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      Author
      Akbudak, K.
      Kayaaslan, E.
      Aykanat, Cevdet
      Date
      2013-02-27
      Source Title
      SIAM Journal on Scientific Computing
      Print ISSN
      1064-8275
      Electronic ISSN
      1095-7197
      Publisher
      Society for Industrial and Applied Mathematics
      Volume
      35
      Issue
      3
      Pages
      C237 - C262
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      Sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it difficult to utilize cache locality effectively in SpMxV computations. In this work, we investigate single-and multiple-SpMxV frameworks for exploiting cache locality in SpMxV computations. For the single-SpMxV framework, we propose two cache-size-aware row/column reordering methods based on one-dimensional (1D) and two-dimensional (2D) top-down sparse matrix partitioning. We utilize the column-net hypergraph model for the 1D method and enhance the row-column-net hypergraph model for the 2D method. The primary aim in both of the proposed methods is to maximize the exploitation of temporal locality in accessing input vector entries. The multiple-SpMxV framework depends on splitting a given matrix into a sum of multiple nonzero-disjoint matrices. We propose a cache-size-aware splitting method based on 2D top-down sparse matrix partitioning by utilizing the row-column-net hypergraph model. The aim in this proposed method is to maximize the exploitation of temporal locality in accessing both input-and output-vector entries. We evaluate the validity of our models and methods on a wide range of sparse matrices using both cache-miss simulations and actual runs by using OSKI. Experimental results show that proposed methods and models outperform state-of-the-art schemes. (c)2013 Society for Industrial and Applied Mathematics
      Keywords
      Cache Locality
      Sparse Matrix
      Matrix-vector Multiplication
      Matrix Reordering, Computational Hypergraph Model
      Hypergraph Partitioning
      Traveling Salesman Problem
      Permalink
      http://hdl.handle.net/11693/11365
      Published Version (Please cite this version)
      http://dx.doi.org/10.1137/100813956
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      • Department of Computer Engineering 1413
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