Galaxies of Supercomputers and their underlying interconnect topologies hierarchies

Galaxies of Supercomputers are defined as tightly interconnected supercomputing resources with latencies of interconnects limited by time-of-flight of the physical optical fibre infrastructure. With the continual increase of the number of peta-scale Supercomputers, and with very fast progress of interconnect technologies, such as Longbow TM from Obsidan Strategics [1] and MetroX from Mellanox [2], allowing RDMA and message passing across global scale distances, as well as research networks growth to attain Terabits per second bandwidth [3], we may imagine certain classess of applications, which would run well on globally federated resources spanning Supercomputer centres across the globe. In order to build a Galaxy of Supercomputers, an optimal hierarchy of interconnect topologies, spanning from an inter-node, intra-rack, inter-rack through to a single Supercomputer centre and up to long-distance, inter-Centres, is needed. We propose a "graph of graphs hierarchy" methodology, and a graph embedding algorithm which may be used to explore colossal-scale space of all possible interconnect topologies. These embedded graphs could be considered simple model for building Galaxy of Supercomputers connecting tens of millions of processing cores residing at the multiple locations of the globe. Here we present just one of our optimal graphs 32k5 ⊗ 32k5 and compare it with existing topologies: K-Computer's TOFU and 5-D torus of BlueGene/Q.Discovery of Optimal Network Topologies By Using Graph Theor