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<p><b>Abstract</b>—The <it>one-to-all broadcast</it> is the most primary collective communication pattern in a multicomputer network. We consider this problem in a wormhole-routed torus which uses the <it>all-port</it> and <it>dimension-ordered</it> routing model. We derive our routing algorithms based on the concept of “span of vector spaces” in linear algebra. For instance, in a 3D torus, the nodes receiving the broadcast message will be “spanned” from the source node to a line of nodes, to a plane of nodes, and then to a cube of nodes. Our results require at most <tmath>$2(k-1)$</tmath> steps more than the optimal number of steps for any square <tmath>$k$</tmath>-D torus. Existing results, as compared to ours, can only be applied to tori of very restricted dimensions or sizes and either rely on an undesirable non-dimension-ordered routing or require more numbers of steps.</p>
Collective communication, interconnection network, one-to-all broadcast, parallel processing, torus, wormhole routing.

Y. Tseng and S. Wang, "Algebraic Foundations and Broadcasting Algorithms for Wormhole-Routed All-Port Tori," in IEEE Transactions on Computers, vol. 49, no. , pp. 246-258, 2000.
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