Sparse matrix-vector multiplication (SpMV) operations are commonly used in various scientific and engineering applications. The performance of the SpMV operation often depends on exploiting regularity patterns in the matrix. Various representations and ...

Efficient processing of Irregular Matrices on Single Instruction, Multiple Data (SIMD)-type architectures is a persistent challenge. Resolving it requires innovations in the development of data formats, computational techniques, and implementations that ...

We describe the application of a communication-reduction technique for the PageRank algorithm that dynamically adapts the precision of the data access to the numerical requirements of the algorithm as the iteration converges. Our variable-precision ...

We investigate outer-product--parallel, inner-product--parallel, and row-by-row-product--parallel formulations of sparse matrix-matrix multiplication (SpGEMM) on distributed memory architectures. For each of these three formulations, we propose a ...

This article derives trade-offs between three basic costs of a parallel algorithm: synchronization, data movement, and computational cost. These trade-offs are lower bounds on the execution time of the algorithm that are independent of the number of ...

We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes both the ...

We present an algorithm for inversion of symmetric positive definite matrices that combines the practical requirement of an optimal number of arithmetic operations and the theoretical goal of a polylogarithmic critical path length. The algorithm reduces ...

Next-generation HPC computing platforms are likely to be characterized by significant, unpredictable nonuniformities in execution time among compute nodes and cores. The resulting load imbalances from this nonuniformity are expected to arise from a ...

The running time of an algorithm depends on both arithmetic and communication (i.e., data movement) costs, and the relative costs of communication are growing over time. In this work, we present sequential and distributed-memory parallel algorithms for ...