In this paper, we give a straight forward, highly e cient, scalable implementation of common matrix multiplication operations. The algorithms are much simpler than previously published methods, yield better performance, and require less work space. MPI implementations are given, as are p erformance r esults on the Intel Paragon system.

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In this paper, we outline a unified approach for building a library of collective communication operations that performs well on a cross-section of problems encountered in real applications. The target architecture is a two-dimensional mesh with worm-hole routing, but the techniques also apply to higher dimensional meshes and hypercubes. We stress a general approach, addressing the need for implementations that perform well for various sized vectors and grid dimensions, including non-power-of-two grids. This requires the development of general techniques for building hybrid algorithms. Finally, our approach also supports collective communication within a group of nodes, which is required by many scalable algorithms. Results from the Intel Paragon system are included.

We address the problem of performing a pipelined broadcast on a mesh architecture. Meshes require a different approach than other topologies, and their very nature puts a tighter bound on the performance that one can hope to achieve. By using the appropriate techniques, however, one can obtain excellent performance for sufficiently long messages. The resulting algorithm will work on meshes of any dimension with any number of nodes. Our model assumes that the mesh is a torus and/or that it has bidirectional links and uses wormhole routing. Performance data from the Cray T3D are included.