Projective Networks: Topologies for Large Parallel Computer Systems

Abstract

The interconnection network comprises a significant portion of the cost of large parallel computers, both in economic terms and power consumption. Several previous proposals exploit large-radix routers to build scalable low-distance topologies with the aim of minimizing these costs. However, they fail to consider potential unbalance in the network utilization, which in some cases results in suboptimal designs. Based on an appropriate cost model, this paper advocates the use of networks based on incidence graphs of projective planes, broadly denoted as Projective Networks. Projective Networks rely on highly symmetric generalized Moore graphs and encompass several proposed direct (PN and demi-PN) and indirect (OFT) topologies under a common mathematical framework. Compared to other proposals with average distance between 2 and 3 hops, these networks provide very high scalability while preserving a balanced network utilization, resulting in low network costs. Overall, Projective Networks constitute a competitive alternative for exascale-level interconnection network design.

Using semidirect products of groups to build classes of interconnection networks

“…We have already heard that the diameter serves as a proxy for worst-case message latency. The combination of low degree and low diameter motivates the study of Moore graphs as potential interconnection networks (see, e.g., [7]).…”

Combining Source-adaptive and Oblivious Routing with Congestion Control in High-performance Interconnects using Hybrid and Direct Topologies

“…Recently, apart from hierarchical topologies, such as Dragonflies [23], Slim-flies [6], or Projective networks [8], hybrid topologies have been proposed to get the benefits from both direct and indirect topologies. In general, the objective of hybrid topologies is to provide high-performance like indirect topologies, but at a similar cost compared to direct topologies.…”

On Random Wiring in Practicable Folded Clos Networks for Modern Datacenters

“…In [9], it was shown that, if all compute nodes inject at the same rate as network links, then T N = ∆u k results in a well balanced network, where k is the average distance, ∆ is the graph degree and u is the average link utilization. Since in RRGs k is close to the diameter D and u is relatively large, which has been experimentally observed to be about 0.7, this expression can be approximated by ∆/D compute nodes per switch.…”