## Revisiting matrix product on master-worker platforms (2006)

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### BibTeX

@TECHREPORT{Pineau06revisitingmatrix,

author = {Jean-françois Pineau and Yves Robert and Frédéric Vivien and Zhiao Shi and Jack Dongarra},

title = {Revisiting matrix product on master-worker platforms},

institution = {},

year = {2006}

}

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### Abstract

This paper is aimed at designing efficient parallel matrix-product algorithms for heterogeneous master-worker platforms. While matrix-product is well-understood for homogeneous 2D-arrays of processors (e.g., Cannon algorithm and ScaLAPACK outer product algorithm), there are three key hypotheses that render our work original and innovative:- Centralized data. We assume that all matrix files originate from, and must be returned to, the master. The master distributes both data and computations to the workers (while in ScaLA-PACK, input and output matrices are initially distributed among participating resources). Typically, our approach is useful in the context of speeding up MATLAB or SCILAB clients running on a server (which acts as the master and initial repository of files).- Heterogeneous star-shaped platforms. We target fully heterogeneous platforms, where computational resources have different computing powers. Also, the workers are connected to the master by links of different capacities. This framework is realistic when deploying the application from the server, which is responsible for enrolling authorized resources.- Limited memory. Because we investigate the parallelization of large problems, we cannot assume that full matrix panels can be stored in the worker memories and re-used for subsequent updates (as in ScaLAPACK). The amount of memory available in each worker is expressed as a given number mi of buffers, where a buffer can store a square block of matrix elements. The size q of these square blocks is chosen so as to harness the power of Level 3 BLAS routines: q = 80 or 100 on most platforms. We have devised efficient algorithms for resource selection (deciding which workers to enroll) and communication ordering (both for input and result messages), and we report a set of numerical experiments on various platforms at École Normale Supérieure de Lyon and the University of Tennessee. However, we point out that in this first version of the report, experiments are limited to homogeneous platforms. 1 1