Publication 2004 Issue No. 4 - April Abstract - A Fault-Tolerant Rearrangeable Permutation Network
A Fault-Tolerant Rearrangeable Permutation Network
April 2004 (vol. 53 no. 4)
pp. 414-426
 ASCII Text x Yuanyuan Yang, Jianchao Wang, "A Fault-Tolerant Rearrangeable Permutation Network," IEEE Transactions on Computers, vol. 53, no. 4, pp. 414-426, April, 2004.
 BibTex x @article{ 10.1109/TC.2004.1268399,author = {Yuanyuan Yang and Jianchao Wang},title = {A Fault-Tolerant Rearrangeable Permutation Network},journal ={IEEE Transactions on Computers},volume = {53},number = {4},issn = {0018-9340},year = {2004},pages = {414-426},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2004.1268399},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - A Fault-Tolerant Rearrangeable Permutation NetworkIS - 4SN - 0018-9340SP414EP426EPD - 414-426A1 - Yuanyuan Yang, A1 - Jianchao Wang, PY - 2004KW - Fault toleranceKW - routingKW - switching networksKW - Clos networksKW - fault modelKW - losing-contact faultKW - rearrangeableKW - permutationKW - cluster computing.VL - 53JA - IEEE Transactions on ComputersER -
Jianchao Wang, IEEE Computer Society
As optical communication becomes a promising networking choice, the well-known Clos network has regained much attention recently from optical switch designers/manufacturers and cluster computing community. There has been much work on the Clos network in the literature due to its uses as optical crossconnects (OXCs) in optical networks and high-speed interconnects in parallel/distributed computing systems. However, little attention has been paid to its fault tolerance capability, an indispensable requirement for any practical high-performance networks. In this paper, we analyze the fault tolerance capability of the three-stage rearrangeable Clos network. We first establish a fault model on losing-contact faults in the switches of the network. Then, under this model, we analyze the fault tolerance capability of the Clos network when multiple such faults present in switches in the input stage, middle stage, and/or output stage of the network. Our results show that the rearrangeable condition on the number of middle stage switches for a fault-free rearrangeable Clos network still holds in the presence of a substantial amount of faults, while a more expensive crossbar network cannot tolerate any single such fault. In particular, we obtain that, for an N \times N Clos network C(m,n,r), where N=nr and m \geq n, it can tolerate any m-1 losing-contact faults arbitrarily located in input/output stage switches, or any m-n losing-contact faults arbitrarily located in middle stage switches, when realizing any permutations. We also demonstrate that, for a given permutation, the network usually can tolerate much more such faults. We then present a necessary and sufficient condition on the losing-contact faults a Clos network can tolerate for any given permutation. We also develop an efficient fault-tolerant routing algorithm for a rearrangeable Clos network based on these results.

[1] J. Lacey, Optical Switching and Its Impact on Optical Networks Proc. Optical Fiber Comm. Conf., Mar. 2001.
[2] L. Lin, E. Goldstein, L. Lunardi, and R. Tkach, Optical Crossconnects for High-Capacity Lightwave Networks J. High Speed Networks, vol. 8, no. 1, pp. 17-34, 1999.
[3] Y. Yang, J. Wang, and C. Qiao, Nonblocking WDM Multicast Switching Networks IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 12, pp. 1274-1287, 2000.
[4] http://www.myri.commyrinet/, 2002.
[5] InfiniBand Architecture Specification 1.0, The InfiniBand Trade Assoc., Oct. 2000, http:/www.infinibandta.org.
[6] C. Clos, A Study of Non-Blocking Switching Networks The Bell System Technical J., vol. 32, pp. 406-424, 1953.
[7] V.E. Benes, Mathematical Theory of Connecting Networks and Telephone Traffic. New York: Academic Press, 1965.
[8] A. Varma and C.S. Raghavendra, Interconnection Networks for Multiprocessors and Multicomputers: Theory and Practice. IEEE CS Press, 1994.
[9] F.K. Hwang, "Control Algorithms for Rearrangeable Clos Networks," IEEE Trans. Comm., vol. 31, pp. 952-954, Aug. 1983.
[10] F.K. Hwang, The Mathematical Theory of Nonblocking Switching Networks. World Scientific, 1998.
[11] H.Y. Lee, F.K. Hwang, and J. Capinelli, A New Decomposition Algorithm for Rearrangeable Clos Interconnection Networks IEEE Trans. Comm., vol. 45, pp. 1572-1578, 1997.
[12] J.D. Carpinelli and C.B. Wang, Performance of a New Decomposition Algorithm for Rearrangeable Fault-Tolerant Clos Interconnection Networks under Sub-Maximal and No-Fault Conditions Advances in Switching Networks, pp. 103-117, 1997.
[13] J.D. Carpinelli and H. Nassar, Fault-Tolerance for Switching Networks, D.-Z. Du and H.Q. Ngo, eds., pp. 1-23, Kluwer Academic Publishers, 2001.
[14] M.P. Haynos and Y. Yang, An Analytical Model on the Blocking Probability of a Fault-Tolerant Network IEEE Trans. Parallel and Distributed Systems, vol 10, no. 10, pp. 1040-1051, Oct. 1999.
[15] Y. Yang and J. Wang, “Wide-Sense Nonblocking Clos Networks under Packing Strategy,” IEEE Trans. Computers, vol. 48, no. 3, pp. 265-284, Mar. 1999.
[16] M.T. Bruggencate and S. Chalasani, “Equivalence between SP2 High-Performance Switches and Three-Stage Clos Networks,” Proc. 25th Int'l Conf. Parallel Processing, pp. I-1–I-8, Bloomingdale, Ill., 1996.
[17] M. Hall, Combinatorial Theory. John Wiley&Sons, 1986.
[18] G.B. Adams, D.P. Agrawal, and H.J. Siegel, A Survey and Comparison of Fault-Tolerant Multistage Interconnection Networks Computer, vol. 20, no. 6, pp. 14-27, June 1987.
[19] K. Padmanabhan and D.H. Lawrie, A Class of Redundant Path Multistage Interconnection Networks IEEE Trans. Computers, vol. 32, no. 12, pp. 1099-1108, Dec. 1983.
[20] R.J. McMillen and H.J. Siegel, Performance and Fault Tolerance Improvements in the Inverse Augmented Data Manipulator Network Proc. Ninth Symp. Computer Architecture, pp. 63-72, Apr. 1982.
[21] C.P. Kruskal and M. Snir, The Performance of Multistage Interconnection Networks for Multiprocessors IEEE Trans. Computers, vol. 32, no. 12, pp. 1091-1098, Dec. 1983.
[22] F.T. Leighton and B.M. Maggs, “Fast Algorithms for Routing around Faults in Multibutterflies and Randomly-Wired Splitter Networks,” IEEE Trans. Computers, vol. 41, no. 5, pp. 578-587, May 1992.
[23] C.C. Fan and J. Bruck, Tolerating Multiple Faults in Multistage Interconnection Networks with Minimal Extra Stages IEEE Trans. Computers, vol. 49, no. 9, pp. 998-1004, Sept. 2000.
[24] S.-W. Seo, T.-Y. Feng, and H.-I. Lee, Permutation Realizability and Fault Tolerance Property of the Inside-Out Routing Algorithm IEEE Trans. Parallel and Distributed Systems, vol. 10, no. 9, pp. 946-957, Sept. 1999.
[25] J.E. Hopcroft and R.M. Karp, An$n^{5/2}$Algorithm for Maximum Matching in Bipartite Graphs SIAM J. Computing, vol. 2, pp. 225-231, Dec. 1973.
[26] R. Cole and J.E. Hopcroft, On Edge Coloring Bipartite Graphs SIAM J. Computing, vol. 11, no. 3, pp. 540-546, Aug. 1982.
[27] R. Cole, K. Ost, and S. Schirra, Edge-Coloring Bipartite Multigraphs in$O(E \log D)$Time Combinatorica, vol. 21, no. 1, pp. 5-12, 2001.

Index Terms:
Fault tolerance, routing, switching networks, Clos networks, fault model, losing-contact fault, rearrangeable, permutation, cluster computing.
Citation:
Yuanyuan Yang, Jianchao Wang, "A Fault-Tolerant Rearrangeable Permutation Network," IEEE Transactions on Computers, vol. 53, no. 4, pp. 414-426, April 2004, doi:10.1109/TC.2004.1268399