A novel P-shape tessellation approach on double-loop networks

Double loop computer networks are widely used in the design and implementation of local area networks and parallel processing architectures. However, the embedding problems on double-loop networks have not been well studied due to the complexity of doubleloop networks. Since the traditional L-shape, designed to compute the diameter of double-loop networks, is not efficient to solve embedding problems, we propose a novel tessellation approach to partition the geometric plane of double-loop networks into a set of parallelogram shaped tiles, called P-shape. Our proposed tessellation technique, P-shape, is a useful theoretical tool for embedding meshes on double-loop networks, and can be extended to analyze other problems as a bridge between regular graphs and double-loop networks.