Optimization of Sparse Distributed Computations

Abstract

We address the problem of the optimization of sparse matrix-vector product (SpMV) on homogeneous distributed systems. For this purpose, we propose three approaches based on partitioning the matrix into row blocks. These blocks are defined by a set of a fixed number of rows and a set of contiguous (resp. non-contiguous) rows containing a fixed number of non-zero elements. These approaches lead to solve some specific NP-hard scheduling problems. Thus, adequate heuristics are designed. We analyse the theoretical performance of the proposed approaches and validate them by a series of experiments. This work represents an important step in an overall objective which is to determine the best-balanced distribution for the SpMV computation on a distributed system. In order to validate our approaches for sparse matrix distribution, we compare them to hypergraph model as well as to PETSc library for SpMV distribution on a homogenous multicore cluster. Experimentations show that our approaches provide performances 2 times better than hypergraph and 49 times better than PETSc.