Wavelength Assignment for Realizing Parallel FFT on Regular Optical Networks

Abstract

Routing and wavelength assignment (RWA) is a central issue to increase efficiency and reduce cost in Wavelength Division Multiplexing (WDM) optical networks. In this paper, we address the problem of wavelength assignment for realizing parallel FFT on a class of regular optical WDM networks. We propose two methods for sequential mapping and shift-reversal mapping of FFT communication pattern to the optical WDM networks concerned. By sequential mapping, the numbers of wavelengths required to realize parallel FFT with 2n nodes on WDM linear arrays, rings, 2-D meshes and 2-D tori are 2n ? 1, 2n ? 1, 2max (k,n ? k) ? 1 and 2max (k,n ? k) ? 1 respectively. By shift-reversal mapping, the numbers of wavelengths required are max (3× 2n ? 3,2), 2n ? 2, max (3× 2max (k,n ? k) ? 3,2) and 2max (k,n ? k) ? 2. These results show that shift-reversal mapping outperforms sequential mapping. Our results have a clear significance for applications because FFT represents a common computation pattern shared by a large class of scientific and engineering problems and WDM optical networks as a promising technology in networking has an increasing popularity.