N-Dimensional Twin Torus Topology

Abstract

Torus topology is one of the preferred topologies for the interconnection network in high-performance clusters and supercomputers. Cost and scalability are some of the properties that make torus suitable for systems with a large number of nodes. The 3D torus is the version more extended due to its excellent nearest neighbor. However, some of the last supercomputers have been built using a torus network with five or six dimensions. To obtain an $nD$ torus, $2n$ ports per node are needed, which 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 previous work we defined and characterized the 3D Twin (3DT) torus which uses two four-port cards per node. In this paper we extend that previous work to define the $n$ -dimensional Twin ( $n$ DT) torus topology. In this case, we formally obtain the optimal port configuration when ( $n$ + 1)-port cards are used instead of $2n$ -port cards. Moreover, we explain how deadlock problem can appear and propose a simple solution. Finally, we include evaluation results which show performance increases when an $nDT$ torus is used instead of an $nD$ torus with fewer dimensions and with the same computational resources.