Area–time trade-offs in arrays with optical pipelined buses

Abstract

A general model for determining the computational efficiency of a particular class of electro-optical systems is described. The model is an abstraction of parallel systems that use digital electronic processors and optical pipelined buses for communication. Minimum requirements in terms of area (volume for three-dimensional structures) and time necessary in order to solve a problem are obtained. Different applications are investigated, and a matching area-time upper bound is given for the barrel-shift problem, simulated on an array with reconfigurable optical pipelined buses. The types of problems for which these lower bounds seem to be realistic are described.

An FPGA-Based Reconfigurable Mesh Many-Core

“…A rather pragmatic way to approach the unrealistic interconnect delay models is to engineer very fast interconnects. In this context, optical models of the reconfigurable mesh were studied, such as the Array with reconfigurable optical buses (AROB) by Pavel and Akl [17] and the Linear Array with a Reconfigurable Pipelined Bus (LARPBS) by Pan and Hamdi [18].…”

“…In each step, two compare-exchange operations are accomplished. First, as specified in lines 6-7, the array connects the even-numbered PEs in a row to their odd-numbered [15][16][17][18][19][20][21][22][23][24][25], the odd-numbered PEs install buses to right hand side even-numbered neighbors, and apply an analogous compare exchange operation. During this step, the nodes in the first and last column of the array remain idle.…”

Using Bus Linearization to Scale the Reconfigurable Mesh

“…The pipelined reconfigurable mesh (PR-Mesh) [24] is a variation of the R-Mesh that uses pipelined optical buses. Other optical models include the array with reconfigurable optical buses (AROB) [20] and the array of processors with pipelined buses using switches (APPBS) [5,9]. One can view the PR-Mesh as a …”

“…Bourgeois and Trahan [5] proved that the classes of languages accepted in constant time with polynomial number of processors by the PR-Mesh, the APPBS [9], and the AROB [20] are the same. Since the PR-Mesh is a restricted version of the AROB, the bus linearization method also works for the AROB with the same overhead as for the PR-Mesh.…”

Simulating a PR-mesh on an LARPBS

“…Some of the one dimensional models include the Linear Array with a Reconfigurable Pipelined Bus System (LARPBS) [2], the Pipelined Optical Bus (POB) [3], the Linear Array with Reconfigurable Optical Buses (LAROB) [14] and the Linear Pipelined Bus (LPB) [4]. Some of the two dimensional (or multidimensional) models include the Pipelined Reconfigurable Mesh (PR-Mesh) [5], the Array with Reconfigurable Optical Buses (AROB) [6], Array Processors with Pipelined Buses (APPB) [7], the Array Processors with Pipelined Buses using Switches (APPBS) [8], the Array with Synchronous Optical Switches (ASOS) [9] and the Reconfigurable Array with Spanning Optical Buses (RASOB) [10].…”