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% less communication volume (30%-38% 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 Terms-Sparse matrices, matrix multiplication, parallel processing, matrix decomposition, computational graph model, graph partitioning, computational hypergraph model, hypergraph partitioning.
Hypergraph partitioning was first applied in sparse matrix decomposition for parallel sparse matrix-vector multiplication by Ç atalyürek and Aykanat in REF .
Hypergraph-partitioning based decomposition for parallel sparse-matrix vector multiplication
IEEE Transactions on Parallel and Distributed Systems
Computer Science