Practical Considerations of Parallel Simulations and Architecture Independent Parallel Algorithm Design

We examine combinatorial properties of a class of hash functions and its application to the simulations of classical models of parallel computation on other models, such as theBSPand theS*PRAM, optimally in communication to within additive lower order terms. The BSP model can serve as a programming paradigm as well; we also examine the implications of architecture independent parallel algorithm design in the context of the BSP model and show how it can lead to portable and scalable implementations of algorithms that can work on a multiplicity of hardware platforms with only recompilation of the source program code. Toward this end, dense Cholesky factorization algorithms are presented and their performance on three parallel hardware platforms, an SGI Power Challenge, IBM SP2, and Cray T3D, is examined and analyzed.