Embedding Cube-Connected Cycles into Grid Network for Minimum Wirelength

Abstract

There is a trade-off problem among diameter, scalability and path length of structure designing in Data Center Network. Therefore, many papers had provided the solution called embeddability, which is an indicator to measure the ability of combining advantages of different networks. This paper considered grid embeddings as an example because they have many applications such as simulation capabilities of a parallel architecture, designing VLSI layout etc. As a modification of the hypercube, Cube-Connected Cycles (CCC) has good symmetry, low diameter and strong connectivity. In this paper, we focused on the minimum wirelength in the linear layout and grid layout of the CCC. Firstly, we analyzed the recursive structure characteristics and properties of CCC. Then, the maximum induced subgraph of CCC is obtained by theoretical analysis. Next, an embedded mode is proposed to layout CCC onto a linear array and we derived an exact formula for the minimum wirelength. Furthermore, we devised an optimal embedding of the n-dimensional CCC onto a grid network.