Adapting shuffle-exchange like parallel processing organizations to work as systolic arrays

Abstract In this paper, parallel algorithms for tree computations and linear recurrence systems of the form y i = a i y i −1 + b i are presented. The algorithms are designed to be executed on a network of parallel processors connected using the shuffle-exchange or cube-connected cycles patterns, where the number of processors is possibly much smaller than the size of the problem being solved. They are the result of illustrating that a graph representing the computation being performed can be restructured to match the given number of processors being employed and the pattern by which the processors are connected. By accepting inputs in a systolic fashion, the algorithms make efficient use of the resources of parallel time and number of processors. Their time performance is T = O( n / P + log P ) when P processors connected by the above mentioned networks are employed, which is the maximum possible speedup for P = O( n /log n ). Thus, the shuffle-exchange and the cube-connected cycles parallel processing organizations can be adapted to work as general systolic systems for the solution of an important class of computational problems.