Three-dimensional Petersen-torus network: a fixed-degree network for massively parallel computers

A two-dimensional (2D) Petersen-torus network is a mesh-class fixed-degree network designed using a Petersen graph, which has a maximum of 10 nodes when the degree is 3 and the diameter is 2 in a (d,k)-graph problem. Here, I propose a new three-dimensional (3D) Petersen-torus network that extends the 2D Petersen-torus network without increasing the degree. The 3D Petersen-torus has the same number of nodes (N). The 3D Petersen-torus is better than the well-known 3D torus and 3D honeycomb mesh in terms of diameter and network cost. The 3D Petersen-torus network is better than the hypercube-like and star graph-like networks in terms of extendibility. Hence, the proposed network may serve as the foundation for realizing a high-performance multicomputer. In this paper, the optimal routing algorithm, Hamilton cycle, and several basic attributes are discussed. Furthermore, a comparison with a mesh-class fixed-degree 3D network is made for degree, diameter, and network cost.