This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Depth-First Search Approach for Fault-Tolerant Routing in Hypercube Multicomputers
April 1990 (vol. 1 no. 2)
pp. 152-159

Using depth-first search, the authors develop and analyze the performance of a routing scheme for hypercube multicomputers in the presence of an arbitrary number of faulty components. They derive an exact expression for the probability of routing messages byway of optimal paths (of length equal to the Hamming distance between the corresponding pair of nodes) from the source node to an obstructed node. The obstructed node is defined as the first node encountered by the message that finds no optimal path to the destination node. It is noted that the probability of routing messages over an optimal path between any two nodes is a special case of the present results and can be obtained by replacing the obstructed node with the destination node. Numerical examples are given to illustrate the results, and they show that, in the presence of component failures, depth-first search routing can route a message to its destination by means of an optimal path with a very high probability.

[1] Y. Saad and M. H. Schultz, "Topological properties of hypercubes,"IEEE Trans. Comput., vol. C-37, pp. 867-872, July 1988.
[2] F. Ercal, J. Ramanujam, and P. Sadayappan, "Task allocation onto a hypercube by recursive mincut bipartitioning," inProc. 3rd Conf. Hypercube Concurrent Comput. Appl., Jan. 1988, pp. 210-221.
[3] M.-S. Chen and K. G. Shin, "Processor allocation in anN-cube multiprocessorusing Gray codes,"IEEE Trans. Comput., vol. C-36, no. 12, pp. 1396-1407, Dec. 1987.
[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. 1226-1244, Dec. 1989.
[5] T. N. Mudge and T. S. Abdel-Rahman, "Vision algorithms for hypercube machines,"J. Parallel Distributed Comput., vol. 4, pp. 79-94, 1987.
[6] T. F. Chan and Y. Saad, "Multigrid algorithms on the hypercube multiprocessor,"IEEE Trans. Comput., vol. C-35, no. 11, pp. 969-977, Nov. 1986.
[7] C. Aykanat, F. Ozguner, F. Ercal, and P. Sadayappan, "Iterative algorithms for solution of large sparse systems of linear equations on hypercubes,"IEEE Trans. Comput., vol. C-37, pp. 1554-1568, Dec. 1988.
[8] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 22-33, Jan. 1985.
[9] NCUBE Corp., "NCUBE/ten: An overview," Beaverton, OR, Nov. 1985.
[10] Intel Corp.,Intel iPSC System Overview, Jan. 1986.
[11] S. L. Johnson and C. T. Ho, "Optimum broadcasting and personalized communication in hypercubes,"IEEE Trans. Comput., vol. C-38, pp.1249-1268, Sept. 1989.
[12] M.-S. Chen and K. G. Shin, "On hypercube fault-tolerant routing using global information," inProc. Fourth Conf. Hypercube Concurrent Comput. Appl., Mar. 6-8, 1989.
[13] C. K. Kim and D. A. Reed, "Adaptive packet routing in a hypercube," inProc. 3rd Conf. Hypercube Concurrent Comput. Appl., Jan. 1988.
[14] J. G. Kuhl and S. M. Reddy, "Distributed fault-tolerance for large multiprocessor system," inProc. 1980 Comput. Architecture Conf., France, May 1980.
[15] T. C. Lee and J. P. Hayes, "Routing and broadcasting in faulty hypercube computers," inProc. 3rd Conf. Hypercube Concurrent Comput. and Appl., vol. I, Jan. 1988, pp. 346-354.
[16] P. Ramanathan and K. G. Shin, "Reliable broadcast in hypercube multicomputers,"IEEE Trans. Comput., vol. C-37, pp. 1654-1656, Dec. 1988.
[17] J. R. Armstrong and F. G. Gray, "Fault diagnosis in a Booleann- cube array of multiprocessors,"IEEE Trans. Comput., vol. C-30, pp. 587-590, Aug. 1981.
[18] 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. 312-317.
[19] J. M. Gordon and Q. F. Stout, "Hypercube message routine in the presence of faults," inProc. 3rd Conf. Hypercube Concurrent Comput. and Appl., Jan. 1988, pp. 318-327.
[20] 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. 90-99.
[21] T. Y. Feng, "A survey of interconnection networks,"IEEE Comput., pp. 12-27, Dec. 1981.
[22] M.-S. Chen, K. G. Shin, and D. D. Kandlur, "Addressing, routing, and broadcasting in hexagonal mesh multiprocessors,"IEEE Trans. Comput., vol. C-39, pp. 10-18, Jan. 1990.
[23] F. Harary,Graph Theory. Reading, MA: Addison-Wesley, 1969.
[24] E. N. Gilbert, "Gray codes and paths on the n-cube,"Bell Syst. Tech. J., vol. 37, pp. 263-267, 1973.
[25] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: Addison-Wesley, 1973.
[26] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: Addison-Wesley, 1974.
[27] C. L. Liu,Introduction of Combinatorial Mathematics. New York: McGraw-Hill, 1968.

Index Terms:
Index Termsfault-tolerant routing; hypercube multicomputers; depth-first search; performance; Hamming distance; obstructed node; destination node; component failures; fault tolerant computing; multiprocessing systems; multiprocessor interconnection networks; performance evaluation
Citation:
M.S. Chen, K.G. Shin, "Depth-First Search Approach for Fault-Tolerant Routing in Hypercube Multicomputers," IEEE Transactions on Parallel and Distributed Systems, vol. 1, no. 2, pp. 152-159, April 1990, doi:10.1109/71.80143
Usage of this product signifies your acceptance of the Terms of Use.