A Unified Theory of Interconnection Network Structure Rev Ed
A Unified Theory of Interconnection Network Structure Rev Ed
Clyde Kruskal
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(See [12], [16], or [19] for a proof of their isomorphism. ) Ultracomputer Note 106 Page 7 It turns out that these networks are obtained by slightly varying the naming scheme that yields the baseline network: the two address parts may be exchanged, and each of them may be reversed (Figures 9b-9f). If a node s is connected to a node s' via an edge that has label 8 at its tail and label e at its head then dis') = d{s)b and a(^) = a. Is')e. (1) The baseline naming scheme associates to each switch ...the address da.. Thus, in the baseline network, a node ;/ at stage / with label a-^, . . . , a^_2, € is connected via an edge with labels 8, e to a node at stage i+l with label a^, . . . , a. -_-^, h, (Xi, . . . , a^_2, for 8 = 0, . . . , outdegree{u) — \. (2) The reverse baseline naming scheme associates to each switch the address dd. Nodes at stage / with label a-, ^, . . . , a„_, _;^ ^, 0.^-1 + 1, ■ . ■ . "„-! are connected to nodes at stage /+1 with labels a^, . . . , a^_^_■^, OL^_^ + ■^, .
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