PolarFly: A Cost-Effective and Flexible Low-Diameter Topology

PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks

“…Unfortunately, the largest known graphs for 𝐷 > 2 and 𝑑 > 2 are much smaller in size than the Moore bound. Some diameter-2 networks such as Polarfly [25] and Slimfly [7] do come close to the Moore bound. However, the scale of these networks is limited by the small diameter-2 Moore bound (𝑑 2 + 1 for radix 𝑑).…”

“…We propose a new family of network topologies called PolarStar that extends PolarFly [25] to large diameter-3 networks using a mathematical construct called the star product.…”

“…Throughout the paper, we discuss desirable properties of network topologies and evaluate various networks on their basis. We analyze Slimfly [7], PolarFly [25], Dragonfly [24], HyperX [2], MegaFly [16,37], SpectralFly [40] and widely used three stage Fat-trees. A summary of the evaluation is given in Table 2.…”

“…Scalability: A network's scale depends on its diameter and Moorebound efficiency (proximity to Moore bound for the given degree and diameter). Diameter-2 networks such as PolarFly [25] asymptotically approach the Moore bound but are limited in scale as the bound itself is small. Three-stage Fat-trees scale similarly to diameter-2 networks.…”

“…In particular, since this family of graphs asymptotically approaches the Moore bound, any improvement to the choice for 𝐺 would be small for the radixes of interest. As seen in PolarFly [25], ER graphs also exhibit a modular layout, high bisection bandwidth and other desirable networking properties.…”