On simulations of linear arrays, rings and 2D meshes on Fibonacci cube networks

The Fibonacci cube was proposed recently as an interconnection network. It has been shown that this new network topology possesses many interesting properties that are important in network design and applications. This paper addresses the following network simulation problem: Given a linear array, a ring or a two-dimensional mesh, how can be assign its nodes to the Fibonacci cube nodes so as to keep their adjacent nodes near each other in the Fibonacci cube. The authors first show a simple fact that there is a Hamiltonian path in any Fibonacci cube. They prove that any ring structure can be embedded into its corresponding optimum Fibonacci cube (the smallest Fibonacci cube with at least the number of nodes in the ring) with dilation 2, which is optimum for most cases. Then, they describe dilation 1 embeddings of a class of meshes into their corresponding optimum Fibonacci cubes. Finally, it is shown that an arbitrary mesh can be embedded into its corresponding optimum or near-optimum Fibonacci cube with dilation 2