Toward optimal complete exchange on wormhole-routed tori

Abstract

In this paper, we propose new routing schemes to perform all-to-all personalized communication (or known as complete exchange) in wormhole-routed, one-port tori. In the literature, some algorithms are optimal in only one of startup and transmission costs, while some, although are asymptotically optimal in both costs, will incur much larger constants associated with the costs. Our algorithms use both asymptotically optimal startup and transmission time on tori of equal size along each dimension. The schemes are characterized by: (i) the use of gather-scatter tree to achieve optimality in startup time, (ii) the enforcement of shortest paths in routing messages to achieve optimality in transmission time, (iii) the application of network-partitioning techniques to reduce the constant associated with the transmission time, and (iv) the dimension-by-dimension and gather-scatter-tree approach to make possible applying the schemes to non-square, any-size tori. Numerical analysis and experiment both show significant improvement on total communication latency over existing results.