Interleaving Partitions of Systolic Algorithms for Programming Distributed Memory Multiprocessors

In this paper we present a systematic method for mapping systolizable problems onto Distributed Memory Multiprocessors. A systolizable problem is a problem for which it is possible to design a Systolic Algorithm. As a first stage, we design a Systolic Algorithm for the problem to be solved. Then, different transformations are applied to this Systolic Algorithm in order to adapt it to the available Distributed Memory Multiprocessor. One of these transformations is what we call band interleaving. This transformation which is the main contribution of this paper permits to increase the granularity of the parallel algorithm reducing in this way the communication requirements. We will show how the proposed transformations modify the original sequential code in order to obtain the parametrized code for each Processing Element of the Distributed Memory Multiprocessor. The method is illustrated with an example consisting in the design of a parallel algorithm to solve a triangular system of equations on a Distributed Memory Multiprocessor System with a ring topology. Some measurements of performance are presented for the case of a Transputerbased network. 1