Abstract
This paper presents a new approach to the joint construction of topologies ofdiameter-optimal circulant networks \(C(N; \pm 1, \pm s_2)\) and optimal routing algorithms of complexity \(O(1)\) implemented for them. New routing algorithms are based on the use ofscalable parameters of \(L\) -shaped patterns in a dense packing of graphs on the plane for families ofoptimal networks. The scalability of the parameters of \(L\) -shaped templates for many families of optimal networks \(C(N; \pm 1, \pm s_2)\) has been proven, analytical formulas for the dependence of these parameterson the diameter of the graphs have been obtained, reducing the time for setting up the routingalgorithm at the preliminary stage from \(O (\log N)\) to \(O(1)\) . A comparison of the new routing algorithm with the optimal routingalgorithm known in the literature showed its greater efficiency by an average of 10 percent interms of time spent on routing in families of optimal graphs. Due to their good scalability andease of routing, optimal degree-four circulant networks are of interest as efficient and reliablecommunication networks for networks-on-chip, multiprocessor supercomputer systems,telecommunications network structures, and neural communication networks.
