Realizing Fault-Tolerant Interconnection Networks Via Chaining
IEEE Transactions on Computers - Fault-Tolerant Computing
IEEE/ACM Transactions on Networking (TON)
SPDP '95 Proceedings of the 7th IEEE Symposium on Parallel and Distributeed Processing
On a Class of Multistage Interconnection Networks
IEEE Transactions on Computers
The Journal of Supercomputing
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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.