Publication 2000 Issue No. 3 - March Abstract - Algebraic Foundations and Broadcasting Algorithms for Wormhole-Routed All-Port Tori
Algebraic Foundations and Broadcasting Algorithms for Wormhole-Routed All-Port Tori
March 2000 (vol. 49 no. 3)
pp. 246-258
 ASCII Text x San-Yuan Wang, Yu-Chee Tseng, "Algebraic Foundations and Broadcasting Algorithms for Wormhole-Routed All-Port Tori," IEEE Transactions on Computers, vol. 49, no. 3, pp. 246-258, March, 2000.
 BibTex x @article{ 10.1109/12.841128,author = {San-Yuan Wang and Yu-Chee Tseng},title = {Algebraic Foundations and Broadcasting Algorithms for Wormhole-Routed All-Port Tori},journal ={IEEE Transactions on Computers},volume = {49},number = {3},issn = {0018-9340},year = {2000},pages = {246-258},doi = {http://doi.ieeecomputersociety.org/10.1109/12.841128},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Algebraic Foundations and Broadcasting Algorithms for Wormhole-Routed All-Port ToriIS - 3SN - 0018-9340SP246EP258EPD - 246-258A1 - San-Yuan Wang, A1 - Yu-Chee Tseng, PY - 2000KW - Collective communicationKW - interconnection networkKW - one-to-all broadcastKW - parallel processingKW - torusKW - wormhole routing.VL - 49JA - IEEE Transactions on ComputersER -

Abstract—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.

Index Terms:
Collective communication, interconnection network, one-to-all broadcast, parallel processing, torus, wormhole routing.
Citation:
San-Yuan Wang, Yu-Chee Tseng, "Algebraic Foundations and Broadcasting Algorithms for Wormhole-Routed All-Port Tori," IEEE Transactions on Computers, vol. 49, no. 3, pp. 246-258, March 2000, doi:10.1109/12.841128