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Properties of the reverse-exchange interconnection network are used to develop a reconfiguration scheme and a two-pass structure for enhancing the efficiency of a class of multistage interconnection networks. Functional relationships among a class of multistage interconnection networks are first derived. According to the functional relationships, we propose a reconfiguration scheme which enables a network to accomplish various interconnection functions of other networks. Then the admissible permutations along with related recursive control algorithms of the reverse-exchange interconnection network are specified through a set of theorems. Using the reverse-exchange property, we also prove that the algorithms actually work. Finally, we prove that arbitrary permutations can be realized in two passes (or 2 · 1og2N switching steps where N is the network size). By taking advantage of Benes network control algorithms, a way to control the two-pass structure is also developed.