Publication 1999 Issue No. 11 - November Abstract - The Necessary Conditions for Clos-Type Nonblocking Multicast Networks
The Necessary Conditions for Clos-Type Nonblocking Multicast Networks
November 1999 (vol. 48 no. 11)
pp. 1214-1227
 ASCII Text x Yuanyuan Yang, Gerald M. Masson, "The Necessary Conditions for Clos-Type Nonblocking Multicast Networks," IEEE Transactions on Computers, vol. 48, no. 11, pp. 1214-1227, November, 1999.
 BibTex x @article{ 10.1109/12.811110,author = {Yuanyuan Yang and Gerald M. Masson},title = {The Necessary Conditions for Clos-Type Nonblocking Multicast Networks},journal ={IEEE Transactions on Computers},volume = {48},number = {11},issn = {0018-9340},year = {1999},pages = {1214-1227},doi = {http://doi.ieeecomputersociety.org/10.1109/12.811110},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - The Necessary Conditions for Clos-Type Nonblocking Multicast NetworksIS - 11SN - 0018-9340SP1214EP1227EPD - 1214-1227A1 - Yuanyuan Yang, A1 - Gerald M. Masson, PY - 1999KW - Interconnection networksKW - multicast networksKW - routing control strategiesKW - nonblockingKW - necessary conditions.VL - 48JA - IEEE Transactions on ComputersER -

Abstract—Efficient interconnection networks are critical in providing low latency, high bandwidth communication in parallel and distributed computing systems with hundreds or thousands of processors. The well-known Clos network or $v(m,n,r)$ network can be extended to provide full one-to-many or multicast capability. In this paper, we consider several typical routing control strategies for Clos-type nonblocking multicast networks and derive the necessary conditions under which this type of network is nonblocking for arbitrary multicast assignments in the strict sense as well as under these control strategies. The necessary conditions obtained are represented as the number of middle stage switches $m \geq \Theta\left(n {\frac{\log r}{\log \log r}} \right )$. These results match the sufficient nonblocking condition for the currently best available explicitly constructed, constant stage nonblocking multicast network [8], [9], and provide a basis for the optimal design of this type of multicast network.

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Index Terms:
Interconnection networks, multicast networks, routing control strategies, nonblocking, necessary conditions.
Citation:
Yuanyuan Yang, Gerald M. Masson, "The Necessary Conditions for Clos-Type Nonblocking Multicast Networks," IEEE Transactions on Computers, vol. 48, no. 11, pp. 1214-1227, Nov. 1999, doi:10.1109/12.811110