On generalized fat trees

We introduce and analyze a new family of multiprocesser interconnection networks, called generalized fat trees, which include as special cases the fat trees used for the connection machine architecture CM-5, pruned butterflies, and various other fat trees proposed in the literature. The generalized fat trees provide a formal unifying concept to design and analyse a fat tree based architecture. The extended generalized fat tree network XGFT(h; m/sub 1/, ..., m/sub h/; w/sub 1/, ..., w/sub h/) of height h has /spl Pi//sub i=1//sup h/ m/sub i/ leaf processors and the inner nodes serve only as switches or routers. Each non-leaf node in level i has m/sub i/ children and each non-root has w/sub i+1/ parent nodes. The generalized fat trees provide regularity, symmetry, recursive scalability, maximal fault-tolerance, logarithmic diameter bisection scalability, and permit simple algorithms for fault tolerant self-routing and broadcasting. These networks are also versatile, since they can efficiently embed rings, meshes and tori, trees, pyramids and hypercubes.<
>