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Nonblocking k-Fold Multicast Networks
February 2003 (vol. 14 no. 2)
pp. 131-141
Jianchao Wang, IEEE Computer Society

AbstractMulticast communication involves transmitting information from a single source to multiple destinations and is a requirement in high-performance networks. Current trends in networking applications indicate an increasing demand in future networks for multicast capability. Many multicast applications require not only multicast capability, but also predictable communication performance such as guaranteed multicast latency and bandwidth. In this paper, we present a design for a nonblocking k-fold multicast network, in which any destination node can be involved in up to k simultaneous multicast connections in a nonblocking manner. We also develop an efficient routing algorithm for the network. As can be seen, a k-fold multicast network has significantly lower network cost than that of k copies of ordinary 1-fold multicast networks and is a cost effective choice for supporting arbitrary multicast communication.

[1] J. Duato, S. Yalamanchili, and L.M. Ni, Interconnection Networks: An Engineering Approach. Morgan Kauffman, 2003.
[2] B. Mukherjee, Optical Communication Networks. McGraw-Hill, 1997.
[3] 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.
[4] X. Lin, P.K. McKinley,, and L.M. Ni,"Deadlock-Free Multicast Wormhole Routing in 2-D Mesh Multicomputers," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 8, Aug. 1994, pp. 793-804.
[5] R. Libeskind-Hadas, D. Mazzoni, and R. Rajagopalan, “Tree-Based Multicasting in Wormhole-Routed Irregular Topologies,” Proc. Merged 12th Int'l Parallel Processing Symp. and the Ninth Symp. Parallel and Distributed Processing, pp. 244-249, Apr. 1998.
[6] L.M. Ni, “Should Scalable Parallel Computers Support Efficient Hardware Multicast?” Proc. Int'l Workshop Collaboration and Mobile Computing '95 Workshop Challenges for Parallel Processing, pp. 2-7, 1995.
[7] P. Mohapatra and V. Varavithya, “A Hardware Multicast Routing Algorithm for Two-Dimensional Meshes,” Proc. Eighth Symp. Parallel and Distributed Processing, pp. 198-205, Oct. 1996.
[8] H. Xu, Y. Gui, and L.M. Ni, “Optimal Software Multicast in Wormhole-Routed Multistage Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 6, pp. 597-607, 1997.
[9] V. Varavithya and P. Mohapatra, “Asynchronous Tree-Based Multicasting in Wormhole-Switched MINs,” IEEE Trans. Parallel and Distributed Systems, vol. 10, no. 11, pp. 1159-1178, 1999.
[10] R. Sivaram, D.K. Panda, and C.B. Stunkel, “Efficient Broadcast and Multicast on Multistage Interconnection Networks Using Multiport Encoding,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 10, pp. 1004-1028, Oct. 1998.
[11] D. Nassimi and S. Sahni, “Parallel Permutation and Sorting Algorithms and a New Generalized Connection Network,” J. ACM, vol. 29, no. 3, pp. 642-667, July 1982.
[12] G.M. Masson and B.W. Jordan, “Generalized Multi-Stage Connection Networks,” Networks, vol. 2, pp. 191-209, 1972.
[13] F.K. Hwang and A. Jajszczyk, “On Nonblocking Multiconnection Networks,” IEEE Trans. Comm., vol. 34, pp. 1,038-1,041, 1986.
[14] P. Feldman, J. Friedman, and N. Pippenger, “Wide-Sense Nonblocking Networks,” SIAM J. Discrete Math., vol. 1, no. 2, pp. 158-173, May 1988.
[15] C. Lee and A.Y. Oruç, “Design of Efficient and Easily Routable Generalized Connectors,” IEEE Trans. Comm., vol. 43, nos. 2,3, 4, pp. 646-650, 1995.
[16] Y. Yang and J. Wang, “A New Self-Routing Multicast Network,” IEEE Trans. Parallel and Distributed Systems, vol. 10, no. 12, pp. 1299-1316, Dec. 1999.
[17] Y. Yang, G.M. Masson, “Nonblocking Broadcast Switching Networks,” IEEE Trans. Computers, vol. 40, pp. 1,005-1,015, 1991.
[18] Y. Yang, “A Class of Interconnection Networks for Multicasting,” IEEE Trans. Computers, vol. 47, no. 8, pp. 899-906, Aug. 1998.
[19] Y. Yang and G.M. Masson, “The Necessary Conditions for Clos-Type Nonblocking Multicast Networks,” IEEE Trans. Computers, vol. 48, no. 11, pp. 1214-1227, Nov. 1999.
[20] Y. Yang and J. Wang, “On Blocking Probability of Multicast Networks,” IEEE Trans. Comm., vol. 46, no. 7, pp. 957-968, July 1998.
[21] C. Clos, “A Study of Non-Blocking Switching Networks,” The Bell System Technical J., vol. 32, pp. 406-424, 1953.
[22] V.E. Benes, “Heuristic Remarks and Mathematical Problems Regarding the Theory of Switching Systems,” The Bell System Technical J., vol. 41, pp. 1201-1247, 1962.
[23] MMC Networks, Inc., NP3400,http:/, 2000.
[24] Motorola Inc., C-Port Network Processors,http:/, 2002.
[25] Z. Zhang and Y. Yang, “Performance Analysis of$\big. k{\hbox{-}}{\rm{Fold}}\bigr.$Multicast Networks,” Proc. IEEE GLOBECOM 2002, Nov. 2002.

Index Terms:
Multicast communication, switching networks, switch-based networks, quality-of-service (QoS), nonblocking, routing, routing algorithms.
Yuanyuan Yang, Jianchao Wang, "Nonblocking k-Fold Multicast Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 2, pp. 131-141, Feb. 2003, doi:10.1109/TPDS.2003.1178877
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