Projective Networks: Topologies for Large Parallel Computer Systems

TL;DR

This paper introduces Projective Networks, a new class of interconnection topologies based on incidence graphs of projective planes, offering scalable, balanced, and cost-effective solutions for large parallel computer systems.

Contribution

It proposes a novel network topology framework using incidence graphs of projective planes, addressing unbalance issues in previous large-radix network designs.

Findings

High scalability with average 2-3 hop distances

Balanced network utilization reduces overall costs

Competitive for exascale interconnection networks

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.