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Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication
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DOI：10.1109/71.780863.png)
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In this work, we show that the standard graph-partitioning-based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrix-vector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partitioning problem. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models. Experimental results on a wide range of realistic sparse test matrices confirm the validity of the proposed hypergraph models. In the decomposition of the test matrices, the hypergraph models using PaToH and hMeTiS result in up to 63 percent less communication volume (30 to 38 percent less on the average) than the graph model using MeTiS, while PaToH is only 1.3-2.3 times slower than MeTiS on the average.
Keyword:
sparse matrices
matrix multiplication
parallel processing
matrix decomposition
computational graph model
graph partitioning
computational hypergraph model
hypergraph partitioning
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