Multiprocessor architectures and physical law

We show that all highly symmetrical interconnection topologies for multiprocessors with low diameter require very long interconnect lengths. Therefore, such multicomputers do not scale well in the physical world with 3 dimensions. On the other hand, highly irregular (random) interconnection topologies have a very large subgraph of diameter two and therefore also require very long interconnect lengths. Hence the only scaling topologies for future massively parallel computers are high diameter regular ones, like mesh networks. The techniques used are symmetry properties in terms of orbits of automorphism groups of graphs, and a modern notion of randomness of individual objects, Kolmogorov complexity.<>