Toward optimal complete exchange on wormhole-routed tori

In this paper, we propose new routing schemes to perform all-to-all persona lized communication (or known as complete exchange) in wormhole-routed, one -port tori. On tori of equal size along each dimension, our algorithms use both asymptotically optimal startup and transmission time. The results are characterized by several interesting features: I)the use of gather-scatter tree to achieve optimality in startup time, 2) enforcement of shortest path s in routing messages to achieve optimality in transmission time, 3) applic ation of network-partitioning techniques to reduce the constant associated with the transmission time, and 4) the dimension-by-dimension and gather-sc atter-tree approach to make possible applying the results to nonsquare, any -size tori. In the literature, some algorithms are optimal in only one of s tartup and transmission costs, while some, although asymptotically optimal in both costs, will incur much larger constants associated with the costs. Numerical analysis and experiment both show that significant improvement ca n be obtained by our scheme on total communication latency over existing re sults.