The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.11 - Nov. (2012 vol.23)
pp: 2117-2124
Dajin Wang , Montclair State University, Montclair
ABSTRACT
The crossed cube is a prominent variant of the well known, highly regular-structured hypercube. In [24], it is shown that due to the loss of regularity in link topology, generating Hamiltonian cycles, even in a healthy crossed cube, is a more complicated procedure than in the hypercube, and fewer Hamiltonian cycles can be generated in the crossed cube. Because of the importance of fault-tolerance in interconnection networks, in this paper, we treat the problem of embedding Hamiltonian cycles into a crossed cube with failed links. We establish a relationship between the faulty link distribution and the crossed cube's tolerability. A succinct algorithm is proposed to find a Hamiltonian cycle in a CQ_n tolerating up to n-2 failed links.
INDEX TERMS
Hypercubes, Fault tolerance, Fault tolerant systems, Lead, Joining processes, Proposals, interconnection networks, Crossed cube, embedding, fault tolerance, faulty links, Hamiltonian cycle
CITATION
Dajin Wang, "Hamiltonian Embedding in Crossed Cubes with Failed Links", IEEE Transactions on Parallel & Distributed Systems, vol.23, no. 11, pp. 2117-2124, Nov. 2012, doi:10.1109/TPDS.2012.30
REFERENCES
[1] C.-P. Chang, T.-Y Sung, and L.-H. Hsu, "Edge Congestion and Topological Properties of Crossed Cube," IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 1, pp. 64-80, Jan. 2000.
[2] Q. Dong and X.F. Yang, "Embedding A Long Fault-free Cycle in A Crossed Cube with More Faulty Nodes," Information Processing Letters, vol. 110, no. 11, pp. 464-468, May 2010.
[3] Q. Dong, X. Yang, and J. Zhao, "Fault Hamiltonicity and Fault Hamiltonian-Connectivity of Generalised Matching Networks," Int'l J. Parallel, Emergent and Distributed Systems, vol. 24, no. 5, pp. 455-461, 2009.
[4] K. Efe, "The Crossed Cube Architecture for Parallel Computing," IEEE Trans. Parallel and Distributed Systems, vol. 3, no. 5, pp. 513-524, Sept. 1992.
[5] K. Efe, P.K. Blackwell, W. Slough, and T. Shiau, "Topological Properties of the Crossed Cube Architecture," Parallel Computing, vol. 20, pp. 1763-1775, 1994.
[6] J. Fan, "Diagnosability of Crossed Cubes under the Comparison Diagnosis Model," IEEE Trans. Parallel and Distributed Systems, vol. 13, no. 10, pp. 1099-1104, Oct. 2002.
[7] J. Fan, X. Lin, and X. Jia, "Optimal Path Embedding in Crossed Cubes," IEEE Trans. Parallel and Distributed Systems, vol. 16, no. 12, pp. 1190-1200, Dec. 2005.
[8] J. Fan and X. Lin, "The $t/k$ -Diagnosability of the BC Graphs," IEEE Trans. Computers, vol. 54, no. 2, pp. 176-184, Feb. 2005.
[9] J. Fan, X. Jia, B. Cheng, and J. Yu, "An Efficient Fault-Tolerant Routing Algorithm in Bijective Connection Networks with Restricted Faulty Edges," J. Theoretical Computer Science, vol. 412, no. 29, pp. 3440-3450, 2011.
[10] W.D. Hillis, The Connection Machine. MIT Press, 1985.
[11] J.P. Hayes, T.N. Mudge, and Q.F. Stout, "Architecture of a Hypercube Supercomputer," Proc. Int'l Conf. Parallel Processing, pp. 653-660, Aug. 1986.
[12] S. Horiguchi and M. Konuki, "The Horizontal Rotate Crossed Cube HCQ Interconnection Network," Proc. Int'l Symp. Parallel Architectures, Algorithms and Networks, p. 118, Dec. 1997.
[13] S.-Y. Hsieh and C.-W. Lee, "Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model," SIAM J. Discrete Mathematics, vol. 23, no. 4, pp. 2010-2019, 2010.
[14] S.-Y. Hsieh and N.-W. Chang, "Hamiltonian Path Embedding and Pancyclicity on the Mobius Cube With Faulty Nodes and Faulty Edges," IEEE Trans. Computers, vol. 55, no. 7, pp. 854-863, July 2006.
[15] W.-T. Huang, W.-K. Chen, and C.-H. Chen, "On the Fault-tolerant Pancyclicity of Crossed Cubes," Proc. Ninth Int'l Conf. Parallel and Distributed Systems, p. 483, Dec. 2002.
[16] H.-S. Hung, J.-S. Fu, and G.-H. Chen, "Fault-Free Hamiltonian Cycles in Crossed Cubes with Conditional Link Faults," Information Sciences, vol. 177, no. 24, pp. 5664-5674, Dec. 2007.
[17] Intel Corporation, iPSC System Overview, Jan. 1986.
[18] P. Kulasinghe, "Connectivity of the Crossed Cube," Information Processing Letters, vol. 61, pp. 221-226, Feb. 1997.
[19] P. Kulasinghe and S. Bettayeb, "Embedding Binary Trees Into Crossed Cube," IEEE Trans. Computers, vol. 44, no. 7, pp. 923-929, July 1995.
[20] S. Latifi, S.Q. Zheng, and N. Bagherzadeh, "Optimal Ring Embedding in Hypercubes with Faulty Links," Proc. IEEE 22th Int'l. Symp. Fault-Tolerant Computing, pp. 178-184, July 1992.
[21] M. Ma, G. Liu, and J.M. Xu, "Fault-Tolerant Embedding of Paths in Crossed Cubes," Theoretical Computer Science, vol. 407, nos. 1-3, pp. 110-116, Nov 2008.
[22] C.L. Seitz, "The Cosmic Cube," Comm. ACM, vol. 28, no. 1, pp. 22-23, 1985.
[23] D. Wang, "Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links," J. Parallel and Distributed Computing, vol. 61, pp. 545-564, Apr. 2001.
[24] D. Wang, "On Embedding Hamiltonian Cycles in Crossed Cubes," IEEE Trans. Parallel and Distributed Systems, vol. 19, no. 3, pp. 334-346, Mar. 2008.
[25] J.M. Xu, M. Ma, and M. Lü, "Paths in Möbuis Cubes and Crossed Cubes," Information Processing Letters, vol. 97, no. 3, pp. 94-97, 2006.
[26] H. Yang, X. Yang, and A. Nayak, "A $(4n-9)/3$ Diagnosis Algorithm for Generalised Cube Networks," Int'l J. Parallel, Emergent and Distributed Systems, vol. 25, no. 3, pp. 171-182, 2010.
27 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool