In this paper, we introduce a fault tolerant fully-adaptive self-routing scheme for a class of augmented banyan network. It can provide more multiple paths than the related previous networks between an input/output pair of a network by adding extra links between switching elements in the same stage and extending the self-routing scheme of the banyan network using the topological properties of the banyan network, which are discovered in this paper. Our routing scheme is as simple as that of the banyan network, which is based on the topological relationships among the switching elements (SEs) in the same stage. We show that the SEs in the same stage are arranged regularly, in other words, each stage of the banyan network is constructed with sequences of a cyclic group of SEs, so we can use not only the inter-stage relationships as the banyan network, but also intra-stage relationships among all switching elements for our scheme. We present an algebraic proof to show the correctness of this routing scheme, and an analytic reliability analysis to provide quantitative comparisons with other networks, which shows that the new network is more reliable than the banyan network and other augmented MINs.
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