An Improved Scheme of Wavelength Assignment for Parallel FFT Communication Pattern on a Class of 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 propose an improved scheme of wavelength assignment of parallel FFT communication pattern on a class of regular optical networks. With our new scheme, the numbers of wavelengths required to realize parallel FFT communication pattern with 2n nodes on WDM linear arrays, rings, 2-D meshes and 2-D tori are $\lfloor 2^{n-2}+1\rfloor$ , $\lfloor 2^{n-3}+1 \rfloor$ , $\lfloor 2^{max(k, n-k)-2}+1\rfloor$ and $\lfloor 2^{max(k,n-k)-3}+1\rfloor$ respectively, which are about one-third less for linear arrays and meshes, and a half less for rings and tori, than the known results. Our results have a clear significance for applications because FFT represents a common communication 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.