Torus-Connected Toroids: An Efficient Topology for Interconnection Networks

Recent supercomputers embody hundreds of thousands of compute nodes, and sometimes millions; as such, they are massively parallel systems. Node interconnection is thus critical to maximise the computing performance, and the torus topology has come out as a popular solution to this crucial issue. This is the case, for example, for the interconnection network of the Fujitsu Fugaku, which was ranked world no. 1 until May 2022 and is the world no. 2 at the time of the writing of this article. Here, the number of dimensions used by the network topology of such torus-based interconnects stays rather low: it is equal to three for the Fujitsu Fugaku's interconnect. As a result, it is necessary to greatly increase the arity of the underlying torus topology to be able to connect the numerous compute nodes involved, and this is eventually at the cost of a higher network diameter. Aiming at avoiding such a dramatic diameter rise, topologies can also combine several layers: such interconnects are called hierarchical interconnection networks (HIN). We propose, in this paper, which extends an earlier study, a novel interconnect topology for massively parallel systems, torus-connected toroids (TCT), whose advantage compared to existing topologies is that while it retains the torus topology for its desirable properties, the TCT network topology combines it with an additional layer, toroids, in order to significantly lower the network diameter. We both theoretically and empirically evaluate our proposal and quantitatively compare it to conventional approaches, which the TCT topology is shown to supersede.