Building 3D Torus Using Low-Profile Expansion Cards

Torus is a subclass of direct topologies that was defined in theory to support dimensions. Although recently some supercomputers have been built on a network with five and six dimensions, the most common case is when only three dimensions are implemented. In the market, there are low-profile communication expansion cards that have a reduced number of ports which is not enough to build tori of a certain number of dimensions. In this paper, we will deal with four-port expansion cards. By means of one of these cards per node, a 2-D torus topology could be built, but not a 3-D torus topology. However, two of these cards could be used to build each node of a 3-D torus topology. In this case, two ports are used to interconnect both cards each other, and the other six ports to connect to six neighbor nodes in the 3-D torus. Theoretically, there are several ways of assigning the dimension and direction of the ports. This paper presents a detailed study of the possible port configurations, and under specific network conditions, the best of them is obtained.