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Summary: Hypergraph-Partitioning-Based Decomposition
for Parallel Sparse-Matrix Vector Multiplication
UÈ mit V. CË atalyuÈrek and Cevdet Aykanat, Member, IEEE
AbstractÐIn 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.
Index TermsÐSparse matrices, matrix multiplication, parallel processing, matrix decomposition, computational graph model, graph
partitioning, computational hypergraph model, hypergraph partitioning.
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1 INTRODUCTION
ITERATIVE solvers are widely used for the solution of large,
sparse, linear systems of equations on multicomputers.
Two basic types of operations are repeatedly performed at
each iteration. These are linear operations on dense vectors
and sparse-matrix vector product (SpMxV) of the form
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