Conditional edge-fault Hamiltonicity of augmented cubes

Information Sciences

Volumn 180, Issue 13, 2010, Pages 2596-2617

  Hsieh, Sun Yuan ^a   Cian, Yi Ru ^a  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

Author keywords

Augmented cubes; Fault tolerant embedding; Graph theoretic interconnection networks; Hamiltonian cycles; Hamiltonicity

Indexed keywords

AUGMENTED CUBES; FAULT-TOLERANT EMBEDDING; GRAPH-THEORETIC INTERCONNECTION NETWORKS; HAMILTONIAN CYCLE; HAMILTONICITY;

GEOMETRY; INTERCONNECTION NETWORKS;

HAMILTONIANS;

EID: 77950864654     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.03.005     Document Type: Article

References (45)

1. Akers S.B., and Krishnamurthy B. A group-theoretic model for symmetric interconnection networks. IEEE Transactions on Computers 38 4 (1989) 555-566
2. Akl S.G. Parallel Computation: Models and Methods (1997), Prentice Hall, NJ
3. Araki T., and Kikuchi Y. Hamiltonian laceability of bubble-sort graphs with edge faults. Information Sciences 177 13 (2007) 2679-2691
4. J.C. Bermond (Ed.), Interconnection Networks, Discrete Applied Mathematics, vols. 37-38, 1992 (special issue).
5. Bhuyan L., and Agrawal D.P. Generalized hypercubes and hyperbus structure for a computer network. IEEE Transactions on Computers C-33 (1984) 323-333
6. Chen X.B. Many-to-many disjoint paths in faulty hypercubes. Information Sciences 179 18 (2009) 3110-3115
7. Choudum S.A., and Sunitha V. Augmented cubes. Networks 40 2 (2002) 71-84
8. Cull P., and Larson S.M. The Möbius cubes. IEEE Transactions on Computers 44 5 (1995) 647-659
9. Dong Q., Yang X., and Wang D. Embedding paths and cycles in 3-ary n-cubes with faulty nodes and links. Information Sciences 180 1 (2010) 198-208
10. Dvořák T., and Koubek V. Long paths in hypercubes with a quadratic number of faults. Information Sciences 179 21 (2009) 3763-3771
11. Efe K. The crossed cube architecture for parallel computation. IEEE Transactions on Parallel and Distributed Systems 3 5 (1992) 513-524
12. Fink J., and Gregor P. Long paths and cycles in hypercubes with faulty vertices. Information Sciences 179 20 (2009) 3634-3644
13. Fu J.S. Fault-tolerant cycle embedding in the hypercube. Parallel computing 29 6 (2003) 821-832
14. Fu J.S. Conditional fault-tolerant Hamiltonicity of star graphs. Parallel Computing 33 7-8 (2007) 488-496
15. Fu J.S. Fault-free Hamiltonian cycles in twisted cubes with conditional link faults. Theoretical Computer Science 407 1-3 (2008) 318-329
16. Fu J.S. Hamiltonian connectivity of the WK-recursive network with faulty nodes. Information Sciences 178 12 (2008) 2573-2584
17. P.A.J. Hilbers, M.R.J. Koopman, J.L.A. van de Snepscheut, The twisted cube, in: Proceedings of the Conference on Parallel Architectures and Languages Europe, Parallel Architectures, Lecture Notes in Computer Science, vol. I, 258, 1987, pp. 152-159.
18. Hsieh S.Y., Ho C.W., and Chen G.H. Fault-free Hamiltonian cycles in faulty arrangement graphs. IEEE Transactions on Parallel and Distributed Systems 10 3 (1999) 223-237
19. Hsieh S.Y., Chen G.H., and Ho C.W. Longest fault-free paths in star graphs with vertex faults. Theoretical Computer Science 262 1-2 (2001) 215-227
20. Hsieh S.Y., Chen G.H., and Ho C.W. Longest fault-free paths in star graphs with edge faults. IEEE Transactions on Computers 50 9 (2001) 960-971
21. Hsieh S.Y. Embedding longest fault-free paths onto star graphs with more vertex faults. Theoretical Computer Science 337 1-3 (2005) 370-378
22. Hsieh S.Y. Fault-tolerant cycle embedding in the hypercube with more both faulty vertices and faulty edges. Parallel Computing 32 1 (2006) 84-91
23. Hsieh S.Y., and Shiu J.Y. Cycle embedding of augmented cubes. Applied Mathematics and Computation 191 2 (2007) 314-319
24. Hsieh S.Y., and Lee C.W. Conditional edge-fault hamiltonicity of matching composition networks. IEEE Transactions on Parallel and Distributed Systems 20 4 (2009) 581-592
25. Hsieh S.Y., and Lee C.W. Pancyclicity of restricted hypercube-like networks under the conditional fault model. SIAM Journal on Discrete Mathematics 23 1 (2010) 2010-2019
26. Hsu D.F. Interconnection networks and algorithms. Networks 23 4 (1993) (special issue)
27. Hsu H.C., Chiang L.C., Tan J.J.M., and Hsu L.H. Fault Hamiltonicity of augmented cubes. Parallel Computing 31 1 (2005) 131-145
28. Hung H.S., Chen G.H., and Fu J.S. Fault-free Hamiltonian cycles in crossed cubes with conditional link faults. Information Sciences 177 24 (2007) 5664-5674
29. Kueng T.L., Liang T., Hsu L.H., and Tan J.J.M. Long paths in hypercubes with conditional node-faults. Information Sciences 179 5 (2009) 667-681
30. Lai P.L., and Hsu H.C. Constructing the nearly shortest path in crossed cubes. Information Sciences 179 14 (2009) 2487-2493
31. Leighton F.T. Introduction to Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes (1992), Morgan Kaufmann, San Mateo, CA
32. Ma M., Liu G., and Xu J.M. Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes. Parallel Computing 33 1 (2007) 36-42
33. Ma M.J., Liu G.Z., and Xu J.M. The super connectivity of augmented cubes. Information Processing Letters 106 2 (2008) 59-63
34. J.H. Park, H.C. Kim, H.S. Lim, Fault-Hamiltonicity of hypercube-like interconnection networks, in: Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium, 2005 (IPDPS'05), vol. 1, 2005, pp. 60.1.
35. N. Singhvi, K. Ghose, The Mcube: a symmetrical cube based network with twisted links, in: Proceedings of the 9th International Symposium of Parallel Processing, Honolulu, 1995, pp. 11-16.
36. Tsai C.H. Linear array and ring embeddings in conditional faulty hypercubes. Theoretical Computer Science 314 (2004) 431-443
37. Tsai P.Y., Fu J.S., and Chen G.H. Embedding Hamiltonian cycles in alternating group graphs under conditional fault model. Information Sciences 179 6 (2009) 851-857
38. Tseng Y.C., Chang S.H., and Sheu J.P. Fault-tolerant ring embedding in a star graph with both link and node failures. IEEE Transactions on Parallel and Distributed Systems 8 12 (1997) 1185-1195
39. Wang N.C., Chu C.P., and Chen T.S. A dual-Hamiltonian-path-based multicasting strategy for wormhole-routed star graph interconnection networks. Journal of Parallel and Distributed Computing 62 12 (2002) 1747-1762
40. Wang S., and Lin S. Path embeddings in faulty 3-ary n-cubes. Information Sciences 180 1 (2010) 191-197
41. Wang W.W., Ma M.J., and Xu JM J.M. Fault-tolerant pancyclicity of augmented cubes. Information Processing Letters 103 2 (2007) 52-56
42. Wang N.C., Yen C.P., and Chu C.P. Multicast communication in wormhole-routed symmetric networks with Hamiltonian cycle model. Journal of Systems Architecture 51 3 (2005) 165-183
43. Wu R.Y., Chen G.H., Kuo Y.L., and Chang G.J. Node-disjoint paths in hierarchical hypercube network. Information Sciences 177 19 (2007) 4200-4207
44. Yang P.J., Tien S.B., and Raghavendra C.S. Embedding of rings and meshes onto faulty hypercubes using free dimensions. IEEE Transactions on Computers 43 5 (1994) 608-613
45. Yang X.F., Evans D.J., and Megson G.M. The locally twisted cubes. International Journal of Computer Mathematics 82 4 (2005) 401-413