A Hypergraph-Partitioning Approach for Coarse-Grain Decomposition

We propose a new two-phase method for the coarse-grain decomposition of irregular computational domains. This work focuses on the 2D partitioning 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. This work also introduces the use of multi-constraint hypergraph partitioning, for solving the decomposition problem. The proposed method explicitly models the minimization of communication volume while enforcing the upper bound of p + q - 2 on the maximum number of messages handled by a single processor, for a parallel system with P = p × q processors. Experimental results on a wide range of realistic sparse matrices con.rm the validity of the proposed methods, by achieving up to 25 percent better partitions than the standard graph model, in terms of total communication volume, and 59 percent better partitions in terms of number of messages, on the overall average.