Topological properties of a 2-dimensional torus-connected cycles network
Antoine Bossard · 2022
Modern supercomputers are massively parallel systems: they include hundreds of thousands of compute nodes. Conventional topologies previously used for the interconnection network of these systems, like the hypercube topology, are no longer suitable as they would induce an overly large number of links, in other words an excessively high network degree. Hence, advanced network topologies have been proposed for this purpose. Hierarchical interconnection networks, and especially torus-based ones have proven very popular: several highly ranked supercomputers, such as the world no. 1 as of May 2022, the Fujitsu Fugaku, have been relying on it. The torus-connected cycles topology (TCC) has been introduced after recognising this trend of the supercomputing industry. Several topological properties of TCCs have been shown; for instance, it is known that a TCC is hamiltonian. In this paper, we further focus on showing such topological properties of TCCs. Precisely, we consider in a 2-dimensional k-ary TCC the symmetry property, important for algorithm design, and the crossing number property, which has applications in circuit design and graph visualisation. On the one hand, a 2-dimensional k-ary TCC is shown to be not symmetric, and on the other hand, an upper bound on its crossing number is established. The obtained upper bound is then evaluated by means of a computer experiment.