Visualizing the Topology and Data Traffic of Multi-Dimensional Torus Interconnect Networks

Torus networks are an attractive topology in supercomputing, balancing the tradeoff between network diameter and hardware costs. The nodes in a torus network are connected in a k -dimensional wrap-around mesh where each node has 2k neighbors. Effectively utilizing these networks can significantly decrease parallel communication overhead and in turn the time necessary to run large parallel scientific and data analysis applications. The potential gains are considerable - 5-D torus networks are used in the majority of the top 10 machines in the November 2017 Graph 500 list. However, the multi-dimensionality of these networks makes it difficult for analysts to diagnose ill-formed communication patterns and poor network utilization since human spatial understanding is by and large limited to 3-Ds. We propose a method based on a space-filling Hilbert curve to linearize and embed the network into a ring structure, visualizing the data traffic as flowlines in the ring interior. We compare our method with traditional 2-D embedding techniques designed for high-dimensional data, such as MDS and RadViz, and show that they are inferior to ours in this application. As a demonstration of our approach, we visualize the data flow of a massively parallel scientific code on a 5-D torus network.