SpectralFly: Ramanujan Graphs as Flexible and Efficient Interconnection Networks

TL;DR

SpectralFly is a new HPC interconnection topology based on Ramanujan graphs that offers improved spectral properties, leading to better or comparable network metrics and performance benefits over existing topologies.

Contribution

This work introduces SpectralFly, a novel topology leveraging Ramanujan graphs, demonstrating superior spectral and network properties for HPC interconnects.

Findings

SpectralFly has better diameter and bisection bandwidth than comparable topologies.

SpectralFly shows resilience to link failures.

Simulations indicate performance and cost benefits of SpectralFly.

Abstract

In recent years, graph theoretic considerations have become increasingly important in the design of HPC interconnection topologies. One approach is to seek optimal or near-optimal families of graphs with respect to a particular graph theoretic property, such as diameter. In this work, we consider topologies which optimize the spectral gap. We study a novel HPC topology, SpectralFly, designed around the Ramanujan graph construction of Lubotzky, Phillips, and Sarnak (LPS). We show combinatorial properties, such as diameter, bisection bandwidth, average path length, and resilience to link failure, of SpectralFly topologies are better than, or comparable to, similarly constrained DragonFly, SlimFly, and BundleFly topologies. Additionally, we simulate the performance of SpectralFly on a representative sample of micro-benchmarks using the Structure Simulation Toolkit Macroscale Element Library simulator and study cost-minimizing layouts, demonstrating considerable benefit of the SpectralFly topology.