PVM Implementation of Heterogeneous ScaLAPACK Dense Linear Solvers

Abstract

This paper discusses some algorithmic issues when computing with a heterogeneous network of workstations (the typical poor man's parallel computer). How is it possible to efficiently implement numerical linear algebra kernels like those included in the ScaLAPACK library? Dealing with processors of different speeds requires to use more involved strategies than purely static block-cyclic data distributions. Dynamic data distribution is a first possibility but may prove impractical and not scalable due to communication and control overhead. Static data distributions tuned to balance execution times constitute another possibility but may prove inefficient due to variations in the processor speeds (e.g. because of different workloads during the computation). There is a challenge in determining a trade-off between the data distribution parameters and the process spawning and possible migration (redistribution) policies. We introduce a semi-static distribution strategy that can be refined on the fly, and we show that it is well-suited to parallelizing several kernels of the ScaLAPACK library such as LU and QR decompositions.