An efficient scheme for complete exchange in 2D tori

All-to-all personalized communication, or complete exchange, is at the heart of numerous applications in parallel computing. An efficient complete exchange algorithm is proposed for square 2ⁿ×2 ⁿ wormhole-routed tori. Previous work has only considered complete exchange algorithms for mesh networks. The proposed algorithm effectively uses the bisection bandwidth of a torus, which is twice that for an equal sized mesh, to achieve complete exchange in a time which is almost half of the (best known) complete exchange time on an equal sized mesh