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

Abstract

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 2 k 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 datafiow of a massively parallel scientific code on a 5-D torus network.