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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 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 is 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.