On the scalability of hypergraph models for sparse matrix partitioning

Bora Uçar and Umit V. Çatalyürek

Abstract. We investigate the scalability of the hypergraph-based sparse matrix partitioning methods with respect to the increasing sizes of matrices and number of nonzeros. We propose a method to rowwise partition the matrices that correspond to the discretization of two-dimensional domains with the five-point stencil. The proposed method obtains perfect load balance and achieves very good total communication volume. We investigate the behaviour of the hypergraph-based rowwise partitioning method with respect to the proposed method, in an attempt to understand how scalable the former method is. In another set of experiments, we work on general sparse matrices under different scenarios to understand the scalability of various hypergraph-based one- and two-dimensional matrix partitioning methods.

Key words. Matrix partitioning; hypergraph partitioning; sparse matrix-vector multiplication.