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A new method is presented for distributing data in sparse matrix-vector multiplication. The method is two-dimensional, tries to minimize the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipartitioning of the sparse matrix, each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros. The communication volume caused by the split is minimized. After the matrix partitioning, the input and output vectors are partitioned with the objective of minimizing the maximum communication volume per processor. Experimental results of our implementation, Mondriaan, for a set of sparse test matrices show a reduction in communication volume compared to one-dimensional methods, and in general a good balance in the communication work. Experimental timings of an actual parallel sparse matrix-vector multiplication on an SGI Origin 3800 computer show that a sufficiently large reduction in communication volume leads to savings in execution time.
Vastenhouw et al. (Sat,) studied this question.