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Radix: Every node has O(lg n) links coming out of it.


Here, latency between two nodes is the number of different bits of binary representation of the two nodes, which is O(lg n).

And radix is number of bits of binary representation of a node.


so for an n-dimensional hypercube it is just a projection of the hypercube into 3d space?


Question: What will be the bisection bandwidth of this topology? My guess is O(N) since when the nodes are divided into two sets there are "parallel" links that connect pairs of node across each side.


@yonguaw: Correct. Bisection bandwidth is N/2.


Question: Is this a practical topology? It has a low latency, but there is also a large overhead of laying out the wires since it's difficult to project hypercubes into 3d space. In this example, which one would win?


This topology appears to be directed since all switches essentially consist of one node.


An advantage to this design is that you are directly connected to your N closest neighbors, but a disadvantage is that your machine needs $2^n$ processors to work in this configuration. Processors typically do have $2*n$ processors, so if you wanted to use this configuration, you might need more or less CPUs.