Both hubs and switches resemble star networks. Cut-Through CT routing speeds up communication on the ring and mesh. Using the d phase algorithm on a hypercube is not aided by CT routing, because each communication uses 1 link. For large m, t s and t h contribute less to t. The dual is multinode accumulation.
Every processor is the destination of a single-node accumulation.
The same communication pattern can also do prefix sums. Links all remain busy. Theoretically, S Superlinear speedup can result from cache effects. After divisions on row k, row k must be sent to the other active processors.