High-speed crosstalk-free routing for optical multistage interconnection networks

Multistage interconnection networks (MINs) can be used to construct electro-optic switches. To implement crosstalk-free switching in such a switch, two I/O connecting paths cannot share a common switching element (SE). Thus, a permutation must be decomposed into partial permutations, each being routed through the switch without crosstalk. It was shown that any permutation can be decomposed into two semipermutations, and each is a maximum partial permutation realizable in one pass in an optical Benes network. However, the time complexity of existing decomposition algorithms for realizing connection requests is proportional to permutation size. In this paper, we reexamine the permutation capacity of MINs, present a simpler proof for semipermutation decomposability, and propose a parallel decomposition algorithm of logarithmic time. This algorithm is shown useful for optimally routing crosstalk-free paths in optical Benes networks in high-speed.