Data Compression and Vectorization of Matrix Multiplication on HXDSP

Lectures 1 and 2 Matrix Multiplication and Matrix Inversion 1 Prior Work on Matrix Multiplication

There has been much effort to improve the runtime of matrix multiplication. The trivial algorithm multiplies n×n matrices in O(n) time. Strassen (’69) surprised everyone by giving an O(n) time algorithm. This began a long line of improvements until in 1986, Coppersmith and Winograd achieved O(n). After 24 years of no progress, in 2010 Andrew Stothers, a graduate student in Edinburgh, improved t...

Exploiting Computation-Friendly Graph Compression Methods for Adjacency-Matrix Multiplication

Computing the product of the (binary) adjacency matrix of a large graph with a real-valued vector is an important operation that lies at the heart of various graph analysis tasks, such as computing PageRank. In this paper we show that some well-known Web and social graph compression formats are computation-friendly, in the sense that they allow boosting the computation. In particular, we show t...

Data Distributions for Sparse Matrix Vector Multiplication

Sparse matrix vector multiplication (SpMxV) is often one of the core components of many scientific applications. Many authors have proposed methods for its data distribution in distributed memory multiprocessors. We can classify these into four groups: Scatter, D-Way Strip, Recursive and Miscellaneous. In this work we propose a new method (Multiple Recursive Decomposition (MRD)), which partitio...

Matrix-Matrix Multiplication on Heterogeneous Platforms

Matrix Multiplication on Heterogeneous Platforms

ÐIn this paper, we address the issue of implementing matrix multiplication on heterogeneous platforms. We target two different classes of heterogeneous computing resources: heterogeneous networks of workstations and collections of heterogeneous clusters. Intuitively, the problem is to load balance the work with different speed resources while minimizing the communication volume. We formally sta...