Crosstalk-Free BPC Semi-Permutations Routing in Optical Multistage Interconnection Networks

A semi-permutation is a partial permutation which meets the requirement of using each switch in the first and last stages of a multistage optical network by only one optical signal at a time. It creates the potential for crosstalk-free routing of the whole permutation but for two cycles of a network. The work is concentrated on semi-permutations received as a result of decomposing BPC (bit-permute-complement) permutations needed in many scientific applications. The given O(NlogN) algorithm makes possible constructing transition matrices for semi-permutations of afore said type basing on periodicity of 1's and 0's in columns of the transition matrix for an initial BPC permutation. For routing in accordance with produced matrices modified sliding windows method is used.