Circulant graphs have been extensively investigated over the past 30 years because of their broad application to different fields of theory and practice. Two known surveys on circulant networks including a survey on undirected circulants have been published: by Bermond et al. [Distributed loop computer networks: A survey, J. Parallel Distributed Comput.24 (1995) 2–10] and by Hwang [A survey on multi-loop networks, Theoret. Comput. Sci.299 (2003) 107–121]. The present paper includes the results which have not been presented there, in particular the works of Russian researchers, and also a lot of new results obtained in the area of research of circulant networks. We focus on the survey connected with study of structural and communicative properties of circulant networks.
The research leading to the results obtained by E. A. Monakhova has been supported in part by the Institute of Computational Mathematics and Mathematical Geophysics SB RAS, budget project number 0315-2019-0006.
A new pair routing algorithm for transmitting messages in multiprocessor systems and networks-on-chip based on circulant networks of arbitrary dimension is proposed. It allows using all reserve shortest paths in the presence of destructive factors (deadlocks, livelocks, starvation, failures) at the nodes and channels of the communication network. A distinctive feature of the proposed algorithm is the absence of using the routing tables with fixed shortest paths when message is transmitted. It becomes possible to determine the set of the shortest paths for routing due to the relative addresses of destination nodes based on a parametric description of the network. Estimates of the number of reserve shortest paths are obtained, and an effective algorithm for using these paths to prevent dynamic topology changes and network congestions is proposed. To reduce the required memory in networks-on-chip with a circulant topology, we proposed a version of the routing algorithm for two-dimensional optimal circulants. We experimentally found the minimum number of reference nodes (nodes containing mapping tables) for them and estimates of memory for mapping tables, as well as the average path length for the routing algorithm using the reference nodes.INDEX TERMS pair routing algorithm, reserve shortest path, circulant network, network-on-chip
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