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 generalized Moore graphs with uniform link utilization 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.

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