Programming Research Group ALGORITHMIC AND PRACTICAL CONSIDERATIONS FOR DENSE MATRIX COMPUTATIONS ON THE BSP MODEL

The Bulk-Synchronous Parallel (BSP) model of computation has been proposed by L.G. Valiant as a unifying and bridging model for the design, analysis and implementation of parallel algorithms that are both scalable and portable, among diverse parallel machines. In this work we present direct BSP algorithms for dense matrix computations such as matrix multiplication, LU decomposition, determinant nding and matrix inversion. Two established distributions of an input matrix among the processors are examined and the particular theoretical and practical merits of each one are discussed. As the BSP model is not just an abstract computational model, it can also be used as a programming paradigm for the implementation of parallel algorithms; towards this direction we implemented the aforementioned algorithms on top of the Oxford BSP Toolset, BSPlib, that provides library support for BSP programming. Our implementations were tested for scalability and portability on a variety of parallel systems that included the SGI Power Challenge, the IBM SP2 and the Cray T3D. Our experimental results support our claims of eeciency, portability and reusabil-ity of the presented algorithms across the named hardware platforms, and reinforce our convictions that the BSP model can also be successfully used as a programming platform or, indeed, as a kind of programming paradigm.