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In recent years, graph theoretic considerations have become increasinglyimportant in the design of HPC interconnection topologies. One approach is toseek optimal or near-optimal families of graphs with respect to a particulargraph theoretic property, such as diameter. In this work, we considertopologies 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, ofSpectralFly topologies are better than, or comparable to, similarly constrainedDragonFly, SlimFly, and BundleFly topologies. Additionally, we simulate theperformance of SpectralFly on a representative sample of micro-benchmarks usingthe Structure Simulation Toolkit Macroscale Element Library simulator and studycost-minimizing layouts, demonstrating considerable benefit of the SpectralFlytopology.

SpectralFly: Ramanujan Graphs as Flexible and Efficient Interconnection Networks