A mathematical model for dynamic memory networks

Abstract

The aim of this paper is to bring together the work done several years ago by M.A. Fiol and the other authors to formulate a quite general mathematical model for a kind of permutation networks known as dynamic memories. A dynamic memory is constituted by an array of cells, each storing one datum, and an interconnection network between the cells that allows the constant circulation of the stored data. The objective is to design the interconnection network in order to have short access time and a simple memory control. We review how most of the proposals of dynamic memories that have appeared in the literature fit in this general model, and how it can be used to design new structures with good access properties. Moreover, using the idea of projecting a digraph onto a de Bruijn digraph, we propose new structures for dynamic memories with vectorial capabilities. Some of these new proposals are based on iterated line digraphs, which have been widely and successfully used by M.A. Fiol and his coauthors to solve many different problems in graph theory.