Near-optimal embeddings of trees into Fibonacci cubes

The Fibonacci cube network was proposed recently as an alternative to the hypercube network. In this paper, we consider the problems of simulating tree and X-tree structures by the Fibonacci cube. Such problems can be characterized as network embedding. There is a big gap between the hypercube and the Fibonacci cube with respect to the availability of routing and embedding results. We present near-optimal embedding results, which show that the Fibonacci cube can simulate trees and X-trees almost as efficiently as the hypercube, even though the Fibonacci cube is a network much sparser than the hypercube.