On two-dimensional sparse matrix partitioning: Models, methods, and a recipe

Umit V. Çatalyürek, Cevdet Aykanat, and Bora Uçar

Abstract. We consider two-dimensional partitioning of general sparse matrices for parallel sparse matrix-vector multiply operation. We present three hypergraph-partitioning based methods, each having unique advantages. The first one treats the nonzeros of the matrix individually and hence produces fine-grain partitions. The other two produce coarser partitions, where one of them imposes a limit on the number of messages sent and received by a single processor, and the other trades that limit for a lower communication volume. We also present a thorough experimental evaluation of the proposed two-dimensional partitioning methods together with the hypergraph-based one-dimensional partitioning methods, using an extensive set of public domain matrices. Furthermore, for the users of these partitioning methods, we present a partitioning recipe that chooses one of the partitioning methods according to some matrix characteristics.

Key words. Sparse matrix partitioning; parallel matrix-vector multiplication; hypergraph partitioning; two-dimensional partitioning; combinatorial scientific computing