On Methods to Align and Access Data Arrays in Parallel Computers

Abstract

We present methods to store and access templates of data arrays in parallel processors with shuffle-exchange-type interconnection networks. For this purpose, we define the class of composite linear permutations. In our method, each element of the data array is stored in the memory module determined by applying a suitable composite linear permutation on its indices. Simple necessary and sufficient criteria to avoid memory conflicts in the access of important templates such as row, column, main diagonal, and square block are given based on the composite linear permutation involved. The criteria so derived also specify the set of permutations to be realized by an interconnection network to avoid network conflicts. In particular, we give the criteria to be satisfied by a scheme of the proposed class to avoid network conflicts during the access of templates, when shuffle-exchange-type networks are used. Almost all the previously known scrambled storage methods are special cases in the class of storage methods presented in this paper.