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M.S. Chen, K.G. Shin, "Adaptive FaultTolerant Routing in Hypercube Multicomputers," IEEE Transactions on Computers, vol. 39, no. 12, pp. 14061416, December, 1990.  
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@article{ 10.1109/12.61061, author = {M.S. Chen and K.G. Shin}, title = {Adaptive FaultTolerant Routing in Hypercube Multicomputers}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {12}, issn = {00189340}, year = {1990}, pages = {14061416}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.61061}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Adaptive FaultTolerant Routing in Hypercube Multicomputers IS  12 SN  00189340 SP1406 EP1416 EPD  14061416 A1  M.S. Chen, A1  K.G. Shin, PY  1990 KW  adaptive fault tolerant routing; hypercube multicomputers; depthfirst search; fault tolerant computing; multiprocessor interconnection networks. VL  39 JA  IEEE Transactions on Computers ER   
A connected hypercube with faulty links and/or nodes is called an injured hypercube. A distributed adaptive faulttolerant routing scheme is proposed for an injured hypercube in which each node is required to know only the condition of its own links. Despite its simplicity, this scheme is shown to be capable of routing messages successfully in an injured ndimensional hypercube as long as the number of faulty components is less than n. Moreover, it is proved that this scheme routes messages via shortest paths with a rather high probability, and the expected length of a resulting path is very close so that of a shortest path. Since the assumption that the number of faulty components is less than n in an ndimensional hypercube might limit the usefulness of the above scheme, a routing scheme based on depthfirst search which works in the presence of an arbitrary number of faulty components is introduced. Due to the insufficient information on faulty components, however, the paths chosen by this scheme may not always be the shortest. To guarantee all messages to be routed via shortest paths, the authors propose to equip every node with more information than that on its own links. The effects of this additional information on routing efficiency are analyzed, and the additional information to be kept at each node for the shortest path routing is determined. Several examples and remarks are given to illustrate the results.
[1] M.S. Chen and K. G. Shin, "Processor allocation in anNcube multiprocessorusing Gray codes,"IEEE Trans. Comput., vol. C36, no. 12, pp. 13961407, Dec. 1987.
[2] L. N. Bhuyan and D. P. Agrawal, "Generalized hypercube and hyperbus structures for a computer network,"IEEE Trans. Comput., vol. C33, no. 4, pp. 323333, Apr. 1984.
[3] T. F. Chan and Y. Saad, "Multigrid algorithms on the hypercube multiprocessor,"IEEE Trans. Comput., vol. C35, no. 11, pp. 969977, Nov. 1986.
[4] M.S. Chen and K. G. Shin, "On relaxed squashed embedding of graphs a into hypercube,"SIAM J. Comput., vol. 18, no. 6, pp. 12261244, Dec. 1989.
[5] B. Becker and H. U. Simon, "How robust is thencube?," inProc. 27th Annu. Symp. Foundations Comput. Sci., Oct. 1986, pp. 283291.
[6] Y. Saad and M. H. Schultz, "Data communication in hypercubes," Dep. Comput. Sci., Yale Univ. Res. Rep. 428/85., 1985.
[7] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 2233, Jan. 1985.
[8] NCUBE Corp., "NCUBE/ten: An overview," Beaverton, OR, Nov. 1985.
[9] E. Chow, H. S. Madan, J. C. Peterson, D. Grunwald, and D. Reed, "Hyperswitch network for the hypercube computer," inProc. 15th Ann. Int. Symp. Comput. Architecture, 1988, pp. 9099.
[10] D. K. Pradhan, "Faulttolerant multiprocessor link and bus network architectures,"IEEE Trans. Comput., vol. C34, no. 1, pp. 3345, Jan. 1985.
[11] J. G. Kuhl and S. M. Reddy, "Distributed faulttolerance for large multiprocessor system," inProc. 1980 Comput. Architecture Conf., France, May 1980.
[12] A.H. Esfahanian and S. L. Hakimi, "Faulttolerant routing in de Bruijn communications networks,"IEEE Trans. Comput., vol. C34, pp. 777788, Sept. 1985.
[13] A. Ghafoor, T. R. Bashkow, and I. Ghafoor, "Faulttolerance and diagnosability of bisectional interconnection networks," inProc. 6th Int. Conf. Distributed Comput. Syst., 1986, pp. 6269.
[14] D. K. Pradhan and S. M. Reddy, "A faulttolerant communication architecture for distributed systems,"IEEE Trans. Comput., vol. C31, no. 9, pp. 863870, Sept. 1982.
[15] M. S. Chen and K. G. Shin, "Message routing in an injured hypercube," inProc. 3rd Conf. Hypercube Concurrent Comput. and Appl., vol. I, Jan. 1988, pp. 312317.
[16] M.S. Chen and K. G. Shin, "On hypercube faulttolerant routing using global information," inProc. Fourth Conf. Hypercube Concurrent Comput. Appl., Mar. 1989, pp. 8386.
[17] C. K. Kim and D. A. Reed, "Adaptive packet routing in a hypercube," inProc. 3rd Conf. Hypercube Concurrent Comput. Appl., Jan. 1988.
[18] S. L. Johnsson and C. T. Ho, "Optimum broadcasting and personalized communication in hypercubes,"IEEE Trans. Comput., vol. C38, no. 9, pp. 12491268, Sept. 1989.
[19] H. Katseff, "Incomplete hypercube,"IEEE Trans. Comput., vol. C37, no. 5, pp. 604608, May 1988.
[20] J. R. Armstrong and F. G. Gray, "Fault diagnosis in a Booleanncube array of microprocessors,"IEEE Trans. Comput., vol. C30, no. 8, pp, 587590, Aug. 1981.
[21] M.S. Chen and K. G. Shin, "Depthfirst search approach for faulttolerant routing in hypercube multicomputers,"IEEE Trans. Parallel Distributed Syst., vol. 1, no. 2, pp. 152159, Apr. 1990.
[22] J. M. McQuillan and D. C. Walden, "The ARPA network design decisions,"Comput. Networks, vol. 1, no. 5, pp. 243289, Aug. 1977.
[23] F. Harary,Graph Theory. Reading, MA: AddisonWesley, 1969.
[24] E. N. Gilbert, "Gray codes and paths on the Ncube,"Bell Syst. Tech. J., vol. 37, pp. 263267, 1973.
[25] Y. Saad and M. H. Schultz, "Topological properties of hypercubes,"IEEE Trans. Comput., vol. C37, no. 7, pp. 867872, July 1988.
[26] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: AddisonWesley, 1974.
[27] K. A. Ross and C. R. B. Wright,Discrete Mathematics. Englewood Cliffs, NJ: PrenticeHall, 1985.
[28] C. L. Liu,Introduction to Combinatorial Mathematics. New York: McGraw Hill, 1968.
[29] K. G. Shin and M.S. Chen, "Performance analysis of distributed routing strategies free of pingpongtype looping,"IEEE Trans. Comput., vol. C36, no. 2, pp. 129137, Feb. 1987.
[30] K. G. Shin and M.S. Chen, "Minimal order loopfree routing strategy,"IEEE Trans. Comput., vol. 39, no. 7, pp. 870881, July 1990.