Peripheral twists for torus topologies with arbitrary aspect ratio

Abstract

A torus is a common topology used in supercomputer networks. Asymmetric Tori suffer from resource usage imbalance, which translates to reduced performance. Twisted Tori employ a twist in the peripheral links of one or more dimensions to improve the topological parameters and overall performance of asymmetric networks. 2D and 3D twisted tori with aspect ratios 2:1 and 2:1:1 have been studied in detail. However, commercial machines do not necessarily employ those aspects ratios. In this work we present an early study of the effect of peripheral link twisting in multidimensional twisted tori with arbitrary aspect ratios. We observe that, in the general case, it is impossible to find a specific twist that minimizes all the interesting topological parameters of the network. We also introduce a requirement for the use of several twists in multidimensional torus with adaptive routing.