Post #2741003
2026-05-11 15:19 UTC
"A Hamiltonian cycle can be constructed by moving across cube dimensions according to the transition sequence in a binary-reflected Gray code. Translating such a cycle to another source node by performing an exclusive-or operation on every node address by the source node index, assuming the first cycle has node zero as its source, creates 2^n = N paths."
Replies (1)
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@theohonohan@graphics.social 2026-05-11 15:21
"These paths cannot be edge-disjoint. But, for all-to-all broadcast, there is no contention between data packets moving along the paths generated by a … Gray code. Moreover, it can be shown that paths generated by rotating the address bits in the Gray code can be used without contention, thus providing n paths for each node. The initial data set M in each node is divided into n packets of approximately equal size. Each subset is then exchanged with packets in all neighboring nodes in each step."