Wavelength assignment of parallel FFT communication pattern on a class of regular optical WDM networks

Wavelength assignment is a key topic in WDM optical interconnection networks. How to realize different parallel communication patterns on optical interconnection networks is a hot research field. Based on the two embedding ways of sequential mapping and shift-reversal mapping, wavelength assignment of realizing parallel FFT communication pattern on a class of regular optical WDM networks is discussed in this paper. By sequential mapping, the numbers of wavelengths required to realize parallel FFT communication pattern with 2ⁿ nodes on WDM linear array, ring, 2-D mesh and 2-D torus are 2^{n - 1} , 2^{n - 1} , 2^{max(k,n - k) - 1} and 2^{max(k,n - k) - 1} respectively. By shift-reversal mapping, the numbers of wavelengths required is max(3×2^{n - 3},2) , 2^{n - 2} , max(3×2^{max(k,n - k) - 3},2) and 2^{max(k,n - k) - 2}. These results show that shift-reversal mapping outperforms sequential mapping.