Abstract:
As a hypercube variation, the crossed cube has some superior properties over the hypercube. For example, the diameter of the crossed cube is approximately half that of the hypercube; the complete binary tree with 2\+ n -1 nodes can be embedded into the n \|dimensional crossed cube with dilation 1, etc.. So it is attractive in the parallel processing area. However, similar to the hypercube, it is necessary to double the number of nodes to upgrade the crossed cube. In order to solve this problem, a kind of interconnection networks, named the super crossed cubes(SCC), is proposed. It is proved that the SCC well retain the advantageous properties that the crossed cube possesses in the respect of the node degrees, the diameter, and the connectivity, and it only needs to add arbitrary number of nodes to upgrade the SCC. The ability of the SCC to simulate a kind of important parallel architectures—ring networks—is discussed by using the graph\|embedding technique in this paper. It is proved that any cycle with length 4 through N are all able to be embedded with dilation 1 into the SCC of N nodes. Thus, it is shown that the ability of the SCC to simulate ring networks is the same as the crossed cube.