Abstract
We propose a new hypergraph model for the decomposition of irregular computational domains. This work focuses on the decomposition of sparse matrices for parallel matrix-vector multiplication. However, the proposed model can also be used to decompose computational domains of other parallel reduction problems. We propose a "fine-grain" hypergraph model for two-dimensional decomposition of sparse matrices. In the proposed fine-grain hypergraph model, vertices represent nonzeros and hyperedges represent sparsity patterns of rows and columns of the matrix. By partitioning the fine-grain hypergraph into equally weighted vertex parts (processors) so that hyperedges are split among as few processors as possible, the model correctly minimizes communication volume while maintaining computational load balance. Experimental results on a wide range of realistic sparse matrices confirm the validity of the proposed model, by achieving up to 50 percent better decompositions than the existing models, in terms of total communication volume.