A transformative approach to the partitioning of processor arrays

Abstract

The paper describes the systematic design of processor arrays with a given dimension and a given number of processing elements. The unified approach to the solution of this problem called partitioning is based on the following concepts: (1) Algorithms and processor arrays are represented by (piecewise regular) programs. (2) The concept of stepwise refinement of programs is used to solve the partitioning problem by applying a sequence of provably correct program transformations. In contrary to other approaches, nonperfect tilings may be considered. The parameters of the introduced program transformations enable the realization of different partitioning schemes. (3) It is shown that the class of piecewise regular programs is closed under partitioning.<>