Gaussian elimination on hypercubes

Abstract : Several implementations of the Gaussian elimination algorithm are compared for solving dense linear systems on hypercube parallel processors. Two classes of methods: methods that require to move the elimination row (or column) to all processors before the elimination proceeds, and methods that require only moving data to nearest neighbors. Algorithms of the second class, which are called pipelined algorithms, require only a ring or grid structure which is embedded into the hypercube. One of the main conclusions is that for Gaussian elimination the addtional connectivity of the hypercube topology over that a two dimensional grid of processors does not help much in improving efficiency. Another result of the analysis is that there is little reason for using row or column typle algorithms instead of grid algorithms. One of the goals of the paper is also to show a simple model of complexity analysis at work, by comparing the estimated times that it provides with the actual execution times.