Optimal Configuration for N-Dimensional Twin Torus Networks

Torus topology is one of the most common topologies used in the current largest supercomputers. Although 3D torus is widely used, recently some supercomputers in the Top500 list have been built using networks with topologies of five or six dimensions. To obtain an nD torus, 2n ports per node are needed. These ports can be offered by a single or several cards per node. In the second case, there are multiple ways of assigning the dimension and direction of the card ports. In a previous work we proposed the 3D Twin (3DT) torus which uses two 4-port cards per node, and obtained the optimal port configuration. This paper extends and generalizes that work in order to obtain the optimal port configuration when n dimensions are considered. Thus, the nDT torus topology is presented and defined, and a detailed formal analysis leads to the optimal port configuration. Finally, performance results are included.