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R.A. Rowley, B. Bose, "FaultTolerant Ring Embedding in de Bruijn Networks," IEEE Transactions on Computers, vol. 42, no. 12, pp. 14801486, December, 1993.  
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@article{ 10.1109/12.260637, author = {R.A. Rowley and B. Bose}, title = {FaultTolerant Ring Embedding in de Bruijn Networks}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {12}, issn = {00189340}, year = {1993}, pages = {14801486}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.260637}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  FaultTolerant Ring Embedding in de Bruijn Networks IS  12 SN  00189340 SP1480 EP1486 EPD  14801486 A1  R.A. Rowley, A1  B. Bose, PY  1993 KW  fault tolerant computing; hypercube networks; faulttolerant ring embedding; de Bruijn networks; multiprocessor network; multiple node (processor) failures; prime power; Hamiltonian cycle. VL  42 JA  IEEE Transactions on Computers ER   
A method of embedding a ring in a dary de Bruijn multiprocessor network in the event of multiple node (processor) failures is presented. In particular, the algorithm guarantees that a (2/sup n/n1)node ring will be found in a binary de Bruijn network with a single faulty node, where 2/sup n/ is the total number of nodes in the network. It is also shown that a (d/sup n/1)node ring can always be found in the presence of d1 link failures, when d is a prime power and the network contains d/sup n/ nodes. The latter is accomplished by constructing d1 edgedisjoint cycles each of length d/sup n/1. A modification of the graph that allows it to admit a Hamiltonian cycle in the event of d1 edge failures is also discussed.
[1] B. Alspach, JC. Bermond, and D. Sotteau, "Decomposition into cycles I: Hamiltonian decompositions," inCycles and Rays, G. Hahn, G. Sabidussi, and R. E. Woodrow, Eds. Kluwer Academic, 1990, pp. 918.
[2] F. Annexstein, "Fault tolerance of hypercubederivative networks," inProc. 1st Annu. ACM Symp. Parallel Algorithms Architectures, 1989, pp. 179188.
[3] M. Atallah and U. Vishkin, "Finding Euler tours in parallel,"J. Syst. Sci., vol. 29, pp. 330337, 1984.
[4] JC. Bermond and C. Peyrat, "de Bruijn and Kautz networks: A competitor for the hypercube?," inHypercube and Distributed Computers, F. Andréand J. P. Verjus, Eds. Holland: Elsevier, 1989.
[5] J. Bruck, R. Cypher, and CT. Ho, "Faulttolerant de Bruijn and shuffleexchange networks," IBM Tech. Rep. RJ 8547, Dec. 1991.
[6] O. Collins, F. Pollara, S. Dolinar, and R. McEliece, "VLSI decomposition of the de Bruijn graph," JPL Telecommunications and Data Acquisition Rep. 42100, Feb. 1990, pp. 180190.
[7] N. G. de Bruijn, "A combinatorial problem,"Proc. Koninklijke Nederlandsche Akademie van Wetenschappen, vol. 49, pp. 758764, 1946.
[8] A.H. Esfahanian and S. L. Hakimi, "Faulttolerant routing in de Bruijn communications networks,"IEEE Trans. Comput., vol. C34, pp. 777788, Sept. 1985.
[9] H. Fredricksen, "A survey of full length nonlinear shift register cycle algorithms,"SIAM Review, vol. 24, pp. 195221, 1982.
[10] R. Gould,Graph Theory. Menlo Park, CA: Benjamin/Cummings, 1988.
[11] F. Harary,Graph Theory. Reading, MA: AddisonWesley, 1969.
[12] N. Homobono and C. Peyrat, "Fault tolerant routings in de Bruijn and Kautz networks,"Discrete Applied Mathematics, vol. 24, pp. 179186, 1989.
[13] M. Imase, T. Soneoka, and K. Okada, "Connectivity of regular directed graphs with small diameters,"IEEE Trans. Comput., vol. C34, pp. 267273, Mar. 1985.
[14] M. Imase, T. Soneoka, and K. Okada, "Faulttolerant processor interconnection networks,"Systems and Computers in Japan, vol. 17, pp. 2130, 1986.
[15] A. Lempel, "On a homomorphism of the de Bruijn graph and its application to the design of feedback shift registers,"IEEE Trans. Comput., vol. C19, pp. 439442, Dec. 1970.
[16] R. J. McEliece,Finite Fields for Computer Scientists and Engineers. Boston, MA: KIuwer Academic, 1987.
[17] B. Obrenic, "Embedding de Bruijn and shuffleexchange graphs in five pages," inProc. 3rd ACM Symp. Parallel Algorithms and Architectures, 1991, pp. 137146.
[18] D. K. Pradhan, "Interconnection topologies for faulttolerant parallel and distributed architectures," inProc. 10th Int. Conf. Parallel Processing, 1981, pp. 238242.
[19] D. K. Pradhan and S. M. Reddy, "A faulttolerant communication architecture for distributed systems,"IEEE Trans. Comput., vol. C31, pp. 863869, Sept. 1982.
[20] M. R. Samatham and D. K. Pradhan, "The de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI,"IEEE Trans. Comput., vol. C38, pp. 567581, Apr. 1989.
[21] M. R. Samatham and D. K. Pradhan, "Corrections to the de Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI,"IEEE Trans. Comput., vol. C40, pp. 122123, Jan. 1991.
[22] M. L. Schlumberger, "DeBruijn communication networks," Ph.D. dissertation, Stanford Univ., Stanford, 1974.
[23] D. Barth, J. Bond, and A. Raspaud, "Compatible Eulerian circuits inKn**," Tech. Rep. 9313, LaBRIUniversitéBordeaux I, Bordeaux, France.
[24] R. Rowley and B. Bose, "On the number of disjoint Hamiltonian cycles in de Bruijn graphs," Tech. Rep. 938009, Dept. of Comput. Sci., Oregon State Univ., 1993.
[25] R. Rowley and B. Bose, "A distributed algorithm for finding a faultfree cycle in a de Bruijn network," inProc. ISCA Int. Conf. Parallel and Distributed Computing Syst., 1993, pp. 263266.