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## Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip

In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest routes between the two nodes based on coordinates are formulated. A technique for calculating optimal network configurations is described. Dense states of the network when all neighborhoods of the central node are filled with nodes and the network has the smallest diameter are defined. It is shown that with an equal number of nodes, the diameter of the circulant is two times smaller than the diameter of the 2D mesh. This is due to the large number of symmetries for the circulant, which leave the set of nodes unchanged. A comparison of communication stability in both topologies in the conditions of failure of network nodes is made, the network behavior under load and failures is modeled, and the advantages of the circulant topology are presented.