Tighter and Broader Complexity Results for Reconfigurable Models

Abstract

A number of models allow processors to reconfigure their local connections to create and alter various bus configurations. This reconfiguration enables development of fast algorithms for fundamental problems, many in constant time. We investigate the ability of such models by relating time and processor bounded complexity classes defined for these models to each other and to those of more traditional models. In this work, (1) we tighten the relations for some of the models, placing them more precisely in relation to each other than was previously known (particularly, the Linear Reconfigurable Network and Directed Reconfigurable Network relative to circuit-defined classes), and (2) we include models (Fusing-Restricted Reconfigurable Mesh and Pipelined Reconfigurable Mesh) not previously considered.

Optimally Scaling Permutation Routing on Reconfigurable Linear Arrays with Optical Buses

“…That is, each model can simulate a step of either of the two other models in constant time, using the same number of processors. (For a more detailed description on the equivalence of models see Trahan et al [10].) We prove the equivalence of the three optical models by a cycle of simulations, one of which is sketched below.…”

Simulating a PR-mesh on an LARPBS

“…The approach of allowing an increase in the number of processors in the simulating model was utilized in the simulation of the Cycle Free Linear Reconfigurable Mesh (CFLR-Mesh) by the LR-Mesh [13][14]. In the simulation of a two dimensional PRMesh on an LARPBS the increase in the number of processors is constant instead of a polynomial increase.…”

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].…”

“…2a. Allowing a polynomial increase in the number of processors, the FR-Mesh is as powerful as the R-Mesh [24], while the LR-Mesh is likely to be less powerful 3 . 3 The set of problems solvable in constant time on the R-Mesh is the same as SL, the class of languages accepted by the symmetric Turing machine in logarithmic space [18].…”

“…The first constructs a faster scaling simulation for the R-Mesh. The second application adapts algorithms designed for the R-Mesh to run on models that use optical buses [19,23,24].…”