Parallel Processing Letters, Vol. 3 No. 4 (1993) 445–456. A UNIFIED APPROACH TO THE DESIGN AND CONTROL OF DYNAMIC MEMORY NETWORKS M.A. FIOL, J. F ` ABREGA, O. SERRA and J.L.A. YEBRA Departament de Matem` atica Aplicada i Telem` atica, Universitat Polit` ecnica de Catalunya, Apdo. 30002, 08080–Barcelona, Spain, e@mail: matjfc@mat.upc.es ABSTRACT A dynamic memory is a storage medium constituted by an array of cells and an interconnection network between them. It is characterized by the constant circulation of the stored data. The objective is to design the interconnection network in order to have small access times and a simple memory control. Several interconnection schemes have been proposed in the literature. This paper presents a quite general model for such structures that greatly facilitates both the design and the control of the memory. Most previous proposals of dynamic memory interconnection networks are particular instances of our model. Moreover, our approach is used to obtain new proposals of interconnection topologies for dynamic memories and fast cyclic shift registers. Namely, a model that optimizes both the access time and the size of the memory and two memory organizations for sequential access are presented. Keywords: Permutation network; Dynamic memory; Shift register memory; Directed graph; Random access; Sequential access. 1. Introduction Bulk memories have traditionally been implemented as magnetic disks and drums, where data are stored at fixed locations on a magnetic surface that moves respect to a read/write mechanism. The use of dynamic storage technologies — such as magnetic bubble or CCD memories— has been proposed to allow a sharp reduction of the access time. This is so because, instead of a mechanical movement, dynamic memories require the movement of the data within the storage medium itself. This already happens in shift register memories, where data are cyclically displaced at time-unit intervals until they reach a read/write port. But with such a structure it is impossible to obtain reduced values of the access time for large memories. Stone [1], [2] was the first to propose a more general model for dynamic memories. Since then there have been many different proposals: Aho and Ullman [3], Iyer and Sinclair [4], Kluge [5], Lenfant [6], Morris, Valiere III and Wisniewski [7], Wong and Tang [8], and the authors [9], [10], [11], [12], [13], [14], [15]. Besides, several patents have been registered [16], [17] and [18]. Most of these organizations are compared in the tutorial of Iyer and Sinclair [19]. A dynamic memory is intended for a set of fixed size data items. The memory consists of cells, each storing one datum, and an interconnection network between them. The network allows the movement of the data from a cell to a neighboring one 1