Algebraic analysis of the topological properties of a banyan network and its application in fault-tolerant switching networks

In this paper, we introduce abstract algebraic analysis of the topological structure of a banyan network, which has become the baseline for most switching networks. The analysis provides the following key results: (1) The switching elements of a switching stage are arranged in order, that is, each stage of a banyan network consists of a series of a cyclic group. (2) The links between switching stages implement a homomorphism relationship in terms of self-routing. Therefore, we can recover the misrouting of a detour fault link by providing adaptive self-routing. (3) The cyclic group of a stage is a subgroup of that of the next stage, so that every stage and its adjacent stage make up a factor group. Based on this analysis, we introduce a cyclic banyan network that is more reliable than other switching networks. We present mathematical analysis of the reliability of the switching network to allow quantitative comparison against other switching networks.