Simulation of Various Networks on Fibonacci Cube Network Topology

Simulation of one interconnection topology by another has several applications in efficient uses of parallel computation networks. The Fibonacci Cube network was proposed recently, [16], [17], (18], [19], [20], [21] as an alternative to the Hypercube networks. Fibonacci Cube networks have rich properties of Fibonacci numbers and hence they can flexibly be decomposed into subgraphs of the same kind. However, there is a tremendous gap between Hypercubes and Fibonacci Cubes with respect to the availability of routing and graph embedding results. These problems have been studied extensively on Hypercubes [2], [4], [6], [7], [24], [25], [27], [28]. In this paper we investigate embeddings of Binary Tree, X-Tree, Arbitrary Binary Tree, Linear Arrays, 2-D Mesh and Ring interconnection networks. The embeddings discussed show that Fibonacci Cube network can efficiently simulate them. They are, in fact, optimum or nearly optimum in both dilation and expansion