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A Broadcast Algorithm for All-Port Wormhole-Routed Torus Networks
August 1996 (vol. 7 no. 8)
pp. 876-885

Abstract—A new approach to broadcast in wormhole-routed two- and three-dimensional torus networks is proposed. The underlying network is assumed to support only deterministic, dimension-ordered unicast routing. The approach extends the graph theoretical concept of dominating nodes by accounting for the relative distance-insensitivity of the wormhole routing switching strategy. The proposed algorithm also takes advantage of an all-port communication architecture, which allows each node to simultaneously transmit messages on different outgoing channels. The resulting broadcast operation is based on a tree structure that uses multiple levels of extended dominating nodes (EDNs). Performance results are presented that confirm the advantage of this method over other approaches.

[1] J. Dongarra et al.,“Document for a standard message-passing interface,” Message Passing Interface Forum, Univ. of Tennessee, Tech. Report CS-93-214, Nov. 1993.
[2] P.K. McKinley et al., "Unicast-Based Multicast Communication in Wormhole-Routed Networks," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 12, Dec. 1994, pp. 1252-1265.
[3] S.L. Johnsson and C.T. Ho,“Spanning graphs for optimum broadcasting and personalizedcommunication in hypercubes,” IEEE Trans. Computers, vol. 38, no. 9, pp. 1,249-1,268, Sept. 1989.
[4] Y.J. Tsai and P.K. McKinkey, “An Extended Dominating Node Approach to Collective Communication in All-Port Wormhole-Routed 2D Meshes,” Proc. Scalable High-Performance Computing Conf., pp. 199–206, Oct. 1994.
[5] W.J. Dally and C.L. Seitz, "The Torus Routing Chip," J. Distributed Computing, vol. 1, no. 3, pp. 187-196, 1986.
[6] L.M. Ni and P.K. McKinley, "A Survey of Wormhole Routing Techniques in Direct Networks," Computer, vol. 26, no. 2, pp. 62-76, Feb. 1993.
[7] W.J. Dally, "Virtual-Channel Flow Control," IEEE Trans. Parallel and Distributed Systems, vol. 3, no. 2, pp. 194-205, Mar. 1992.
[8] W.J. Dally and C.L. Seitz, “Deadlock-Free Message Routing in Multiprocessor Interconnection Networks,” IEEE Trans. Computers, Vol. C-36, No. 5, May 1987, pp. 547-553.
[9] Cray Research Inc., Cray T3D System Architecture Overview Manual, 1993.
[10] M.D. Noakes, D.A. Wallach, and W.J. Dally, "The J-Machine Multicomputer: An Architectural Evaluation," Proc. 20th Ann. Int'l Symp. Computer Architecture, pp. 224-235, May 1993.
[11] A.A. Chien, "A Cost and Speed Model for k-ary n-cube Wormhole Routers," Proc. Hot Interconnects '93Palo Alto, Calif., Aug.5-7, 1993.
[12] Y.-J. Tsai and P.K. McKinley, "A Dominating Set Model for Broadcasting in All-Port Wormhole-Routed 2D Mesh Networks," Proc. ACM Int'l Conf. Supercomputing, pp. 126-135, 1994.
[13] D.F. Robinson, P.K. McKinley,, and B.H.C. Cheng,"Optimal Multicast Communication in Wormhole-Routed Torus Networks," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 11, Oct. 1995, p. 1029-1042.
[14] L.A. Barroso and M. Dubois,“The performance of cache-coherent ring-based multiprocessors,” Proc. 20th Int’l Conf. of Computer Architectures, IEEE Computer Society Press, Apr. 1993, pp. 268-277.
[15] P.K. McKinley, Y.-J. Tsai, and D. Robinson, "Collective Communication in Wormhole-routed Massively Parallel Computers," Computer, vol. 28, no. 12, pp. 39-50, Dec. 1995.
[16] C.-T. Ho and M. Kao, "Optimal Broadcast in All-Port Wormhole-Routed Hypercubes," Proc. 1994 Int'l Conf. Parallel Processing, vol. III, pp. 167-171, Aug. 1994.
[17] J.-Y.L. Park and H.-A. Choi, "Circuit-Switched Broadcasting in Tours and Mesh Networks," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 2, pp. 184-190, Feb. 1996.
[18] J. Peters and M. Syska, "Circuit-Switched Broadcasting in Torus Networks," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 3, pp. 246-255, 1996.

Index Terms:
Broadcast, collective communication, torus, wormhole routing, all-port, dominating set.
Yih-jia Tsai, Philip K. McKinley, "A Broadcast Algorithm for All-Port Wormhole-Routed Torus Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 8, pp. 876-885, Aug. 1996, doi:10.1109/71.532118
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