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Issue No.10 - Oct. (2013 vol.24)
pp: 1951-1960
Chia-Wen Cheng , National Cheng Kung University, Tainan
Chia-Wei Lee , National Cheng Kung University, Tainan
Sun-Yuan Hsieh , National Cheng Kung University, Tainan
A graph $(G)$ is conditional $(k)$-edge-fault Hamiltonian if it remains Hamiltonian after deleting at most $(k)$ edges and each vertex incident to at least two nonfaulty edges. A graph $(G)$ is $(k)$-edge-fault Hamiltonian-connected if it remains Hamiltonian-connected after deleting at most $(k)$ edges. This study shows that the conditional edge-fault Hamiltonicity of the Cartesian product network $(G\times H)$ can be efficiently evaluated given two graphs $(G)$ and $(H)$ that are edge-fault Hamilton-connected and conditional edge-fault Hamiltonian. This study uses the result to evaluate the conditional edge-fault Hamiltonicity of two multiprocessor systems, the generalized hypercubes and the nearest neighbor mesh hypercubes, both of which belong to Cartesian product networks.
Bridges, Hypercubes, Argon, Algorithm design and analysis, Multiprocessing systems, Distributed computing, Educational institutions, graph theoretical interconnection networks, Cartesian product networks, fault-tolerant embedding, Hamiltonicity, Hamiltonian-connectivity
Chia-Wen Cheng, Chia-Wei Lee, Sun-Yuan Hsieh, "Conditional Edge-Fault Hamiltonicity of Cartesian Product Graphs", IEEE Transactions on Parallel & Distributed Systems, vol.24, no. 10, pp. 1951-1960, Oct. 2013, doi:10.1109/TPDS.2012.304
[1] S.G. Akl, Parallel Computation: Models and Methods. Prentice Hall, 1987.
[2] Y.A. Ashir, I.A. Stewart, and A. Ahmed, "Communication Algorithms in $k$ -ary $n$ -Cube Interconnection Networks," Information Processing Letters, vol. 16, no. 1, pp. 43-48, 1997.
[3] Y.A. Ashir and I.A. Stewart, "Fault-Tolerant Embeddings of Hamiltonian Circuits in $k$ -ary $n$ -Cube," SIAM J. Discrete Math., vol. 15, no. 3, pp. 317-328, 2002.
[4] N. Bagherzadeh, "Hamiltonian Path Problems in the On-Line Optimization of Flexible Manufacturing Systems," PhD thesis, Univ. of Technology, reports, 1995.
[5] S. Bettayeb, "On the $k$ -ary Hypercube," Theoretical Computer Science, vol. 140, no. 2, pp. 333-339, 1995.
[6] L.N. Bhuyan and D.P. Agrawal, "Generalized Hypercube and Hyperbus Structures for a Computer Network," IEEE Trans. Computers, vol. C-33, no. 4, pp. 323-333, Apr. 1984.
[7] M.Y. Chang and S.J. Lee, "On the Existence of Hamiltonian Circuits in Faulty Hypercubes," SIAM J. Discrete Math., vol. 4, no. 4, pp. 511-527, 1991.
[8] W.S. Chiue and B.S. Shieh, "On Connectivity of the Cartesian Product of Two Graphs," Applied Math. and Computation, vol. 102, nos. 2/3, pp. 129-137, 1999.
[9] K. Day and A.E. Al-Ayyoub, "The Cross Product of Interconnection Networks," IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 2, pp. 109-118, Feb. 1997.
[10] K. Day and A.E. Al-Ayyoub, "Minimal Fault Diameter for Highly Resilient Product Networks," IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 9, pp. 926-930, Sept. 2000.
[11] J.-S. Fu, "Conditional Fault Hamiltonicity of the Complete Graph," Information Processing Letters, vol. 107, pp. 110-113, 2008.
[12] J.-S. Fu, "Fault-Free Hamiltonian Cycles in Twisted Cubes with Conditional Link Faults," Theoretical Computer Science, vol. 407, nos. 1-3, pp. 318-329, 2008.
[13] S.Y. Hsieh and C.W. Lee, "Conditional Edge-Fault Hamiltonicity of Matching Composition Networks," IEEE Trans. Parallel and Distributed Systems, vol. 20, no. 4, pp. 581-592, Apr. 2009.
[14] S.Y. Hsieh and C.D. Wu, "Optimal Fault-Tolerant Hamiltonicity of Star Graphs with Conditional Edge Faults," J. Supercomputing, vol. 49, no. 3, pp. 354-372, Sept. 2009.
[15] S.Y. Hsieh and C.Y. Wu, "Edge-Fault-Tolerant Hamiltonicity of Locally Twisted Cubes under Conditional Edge Faults," J. Combinatorial Optimization, vol. 9, no 1, pp. 16-30, 2010.
[16] S.Y. Hsieh and T.J. Lin, "Super Fault-Tolerant Hamiltonicity of Product Networks," Proc. IEEE Int'l Symp. Parallel and Distributed Processing with Applications (ISPA '10), 2010.
[17] H.C. Hsu, T.K. Li, J.J.M. Tan, and L.H. Hsu, "Fault Hamiltonicity and Fault Hamiltonian Connectivity of the Arrangement Graphs," IEEE Trans. Computers, vol. 53, no. 1, pp. 39-52, Jan. 2004.
[18] H.S. Hung, G.H. Chen, and J.S. Fu, "Fault-Free Hamiltonian Cycles in Crossed Cubes with Conditional Link Faults," Information Sciences, vol. 177, no. 24, pp. 5664-5674, 2007.
[19] F.T. Leighton, Introduction to Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes. Morgan Kaufmann, 1992.
[20] J.H. Park, H.C. Kim, and H.C. Kim, "Panconnectivity and Pancyclicity of Hypercube-Like Interconnection Networks with Faulty Elements," Theoretical Computer Science, vol. 377, nos. 1-3, pp. 170-180, 2007.
[21] I.A. Stewart and Y. Xiang, "Embedding Long Paths in $k$ -ary $n$ -Cubes with Faulty Nodes and Links," IEEE Trans. Parallel and Distributed Systems, vol. 19, no. 8, pp. 1071-1085, Aug. 2008.
[22] C.H. Tsai, "Linear Array and Ring Embeddings in Conditional Faulty Hypercubes," Theoretical Computer Science, vol. 314, no. 3, pp. 431-443, 2004.
[23] N.C. Wang, C.P. Chu, and T.S. Chen, "A Dual-Hamiltonian-Path-Based Multicasting Strategy for Wormhole-Routed Star Graph Interconnection Networks," J. Parallel and Distributed Computing, vol. 62, no. 12, pp. 1747-1762, 2002.
[24] N.C. Wang, C.P. Yen, and C.P. Chu, "Multicast Communication in Wormhole-Routed Symmetric Networks with Hamiltonian Cycle Model," J. Systems Architecture, vol. 51, no. 3, pp. 165-183, 2005.
[25] Y. Xiang and I.A. Stewart, "Bipancyclicity in K-Ary n-Cubes with Faulty Edges under a Conditional Fault Assumption," IEEE Trans. Parallel and Distributed Systems, vol. 22, no. 9, pp. 1506-1513, Sept. 2011.
[26] Y. Xiang and I.A. Stewart:, "A Multipath Analysis of Biswapped Networks," The Computer J., vol. 54, no. 6, pp. 920-930, 2011.
[27] M.C. Yang Jimmy, J.M. Tan, and L.H. Hsu, "Hamiltonian Circuit and Linear Array Embeddings in Faulty $k$ -ary $n$ -Cubes," J. Parallel and Distributed Computing, vol. 67, no. 4, pp. 362-368, 2007.
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