Decomposing Irregularly Sparse Matrices for Parallel Matrix-Vector Multiplication

In this work, we show the deficiencies of the graph model for decomposing sparse matrices for parallel matrix-vector multiplication. Then, we propose two hypergraph models which avoid all deficiencies of the graph model. The proposed models reduce the decomposition problem to the well-known hypergraph partitioning problem widely encountered in circuit partitioning in VLSI. We have implemented fast Kernighan-Lin based graph and hypergraph partitioning heuristics and used the successful multilevel graph partitioning tool (Metis) for the experimental evaluation of the validity of the proposed hypergraph models. We have also developed a multilevel hypergraph partitioning heuristic for experimenting the performance of the multilevel approach on hypergraph partitioning. Experimental results on sparse matrices, selected from Harwell-Boeing collection and NETLIB suite, confirm both the validity of our proposed hypergraph models and appropriateness of the multilevel approach to hypergraph partitioning.

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