A new scheme to realize crosstalk-free permutations in optical MINs with vertical stacking

Vertical stacking is an alternative for constructing nonblocking multistage interconnection networks (MINs). In this paper, we study the crosstalk-free permutation in rearrangeable, self-routing Banyan-type optical MINs built on vertical stacking and propose a new scheme for realizing permutations in this class of optical MINs, crosstalk-free. The basic idea of the new scheme is to classify permutations into permutation classes such that all permutations in one class share the same crosstalk-free decomposition pattern. By running the Euler-Split based crosstalk-free decomposition only once for a permutation class and applying the obtained crosstalk-free decomposition pattern to all permutations in the class, crosstalk-free decomposition of permutations can be realized in a more efficient way. We show that the number of permutations in a permutation class is huge, enabling the average time complexity of the new scheme to realize a crosstalk-free permutation in an N by N network to be reduced to O(N) from previously O(NlogN)