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Vertical stacking is an interesting technique for creating nonblocking multistage interconnection networks (MINs). The rearrangeable nonblocking optical MINs are attractive since they have lower complexity than their strict nonblocking counterparts. We study the crosstalk-free permutation in rearrangeable nonblocking banyan-type optical MINs built on vertical stacking and provide a scheme for realizing crosstalk-free permutations in this class of optical MINs. The basic idea of our scheme is to decompose a permutation into multiple partial per-mutations based on the idea of Euler tour traversing, and then realize each of partial permutations crosstalk-free in a stacked copy of the MIN so that the full permutation can be realized crosstalk-free in the network in a single pass.