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Algebraic foundations and broadcasting algorithms for wormhole-routed all-port tori

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2 Author(s)
San-Yuan Wang ; Inst. of Comput. Sci. & Inf. Eng., Nat. Central Univ., Chung-Li, Taiwan ; Yu-Chee Tseng

The one-to-all broadcast is the most primary collective communication pattern in a multicomputer network. We consider this problem in a wormhole-routed torus which uses the all-port and dimension-ordered 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 2(k-1) steps more than the optimal number of steps for any square k-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

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Computers, IEEE Transactions on  (Volume:49 ,  Issue: 3 )