Adjacent vertices fault-tolerance fanability of hypercube 陳俐宏、黃鈴玲
E-mail: [email protected]
ABSTRACT
In this paper, we introduce the concepts of fault tolerant fanability. We show that the n-dimensional hypercube Qn are f-adjacent and l edges fault tolerant (n-f-l)*-fanable for n>=3, f+l<=n-2., f<=n-3. And the graph Qn is one node f-adjacent l edge
(n-f-l-1)*-fanable, for f+l<=n-2., f<=n-3.
Keywords : n-dimensional hypercube, fanability.
Table of Contents
封面內頁 簽名頁 授權書...iii 中文摘要...iv 英文摘 要...v 誌謝...vi 目
錄...vii 圖目錄...viii Chapter 1
Introduction...1 Chapter 2 Preliminaries...3 Chapter 3 The f-adjacency l edges fanability of hypercube...4 Section 3.1. f-adjacency...4 Section 3.2. l edges...5 Chapter 4 The 1 node f-adjacency l edges fanability of hypercube...28 Chapter 5 Conclusion...60 Bibliography...61
REFERENCES
[1] C. H. Chang, C. K. Lin, H. M. Huang, and L. H. Hsu, “The super laceability of the hypercubes, ” Information Processing Letters, Vol. 92, pp. 15-21, 2004.
[2] C.C. Chen, C.N. Hung, K.C. Hu, “Edge Fault-tolerant of k*-bifanability for bi- partite Hypercube-like graphs,” Workshop on Combinatorial Mathematics and Computational Theory, Vol. 22, pp. 134-139, 2005.
[3] C.N. Hung, Y. H. Chang, and C. M. Sun, “Longest paths and cycles in fault hypercubes,” Proceedings of the IASTED ICPDCN, pp.
101-110, 2006.
[4] C.D. Park, K.Y. Chwa, “Hamiltonian properties on the class of hypercube-like network,” Information Processing Letters, Vol. 91, pp. 11-17 , 2004.
[5] C. H. Tsai, Jimmy J. M. Tan, T. Liang, and L. H. Hsu, “Fault-tolerant hamil- tonian laceability of hypercubes,” Information Processing Letters, pp. 301-306, 2002.
[6] C. P. Chang, T. Y. Sung, L. H. Hsu, “Edge congestion and topological properties of crossed cubes,” IEEE Trans. Parallel Distrib. Syst, pp.
64-80, 2000.
[7] F.B. Chedid, “On the generalized twisted cube,” Inform. Proc. Lett. 55, pp. 49-52, 1995.
[8] K. Efe, “A variation on the hypercube with lower diameter,” IEEE Trans. on Computers 40, pp. 1312-1316, 1991.
[9] K. Efe, “The crossed cube architecture for parallel computing,” IEEE Trans. Parallel Distrib. Syst, pp. 513-524, 1992.
[10] K. Efe, P.K. Blachwell, W. Slough, T. Shiau, “Topological properties of the crossed cube architecture,” Parallel Comput, pp. 1763-1775, 1994.
[11] A.H. Esfahanian, L.M. Ni, B.E. Sagan, “The twisted n-cube with application to multi-processing,” IEEE Trnas. Computers 40, pp. 88-93, 1991.
[12] P.A.J. Hilbers, M.R.J. Koopman, J.L.A. van de Snepscheut, “The Twisted Cube, in J. Bakker, A. Nijman, P. Treleaven, eds,” PARLE:
Parallel Architectures and Languages Europe, Vol. I: Parallel Architectures, pp. 152-159, 1987.
[13] K.C. Hu, C.N. Hung, C.C. chen, “Edges fault-tolerant Hamiltonian laceability of bipartite hypercube-like networks,” Workshop on Combinatorial Mathematics and Computational Theory, pp. 129-133, 2005.
[14] C.N. Hung, K.C. Hu, “Fault-tolerant Hamiltonian laceability of bipartite hypercube-like networks,” The Proceedings of the 2004 International Computer Symposium, pp. 1145-1149, 2004.
[15] P. Kulasinghe, S. Bettayeb, Embedding, “binary trees into crossed cubes,” IEEE Trans. Comput, pp. 923-929, 1995.
[16] S. Latifi, S. Zheng, N. Bagherzadeh, “Optimal ring embedding in hypercubes with faulty links,” Fault-Tolerant Computing Symp, pp.
178-184, 1992.
[17] F.T. Leighton, “Parallel Algorithms and Architectures Arrays: Trees and Hy- percubes, Morgan Kaufmann, San Mateo,” 1992.
[18] S. Madhavapeddy, I.H. Sudborough, “A topological property of hypercubes: node disjoint paths,” in Proc. of the 2th IEEE Symposium on Parallel and Distributed Processing SPDP, pp. 532-539, 1990.
[19] J.H. Park, “One-to-Many Disjoint Path Covers in a graph with Faulty Element,” COCOON, pp. 329-401, 2004.
[20] J.H. Park, “One-to-one disjoint path covers in recursive circulants,” Journal of KISS 30, pp. 691-698, 2003.
[21] A. Sengupta, “On ring embedding in hypercubes with faulty nodes and links,” Inform. Proc. Lett. 68, pp. 207-214, 1998.
[22] C.H. Tsai, “Linear array and ring embeddings in conditional faulty hypercubes,” Theoretical Computer Science 314, pp. 431-443, 2004.
[23] A.S. Vaidya, P.S.N Rao, S.R. Shankar, “A class of hypercube-like networks,” Proc. Of the 5th Symp. On Parallel and Distributed Processing, IEEE Comput. Soc., Los Alamitos, CA, pp. 800-803, 1993.
[24] M.C. Yang, T.K. Li, J.M. Tan, L.H Hsu, “Fault-tolerant cycle-embedding of crossed cubes,” Inform. Process. Lett, pp. 149-154, 2003.
