Edge-fault-tolerant hamiltonicity of locally twisted cubes under conditional edge faults

Akl SG (1997) Parallel computation: models and methods. Prentice Hall, New York

Ascheuer N (1995) Hamiltonian path problems in the on-line optimization of flexible manufacturing systems. PhD Thesis, University of Technology, Berlin, Germany (also available from ftp://ftp.zib.de/pub/zib-publications/reports/TR-96-03.ps )

Cull P, Larson SM (1995) The Möbius cubes. IEEE Trans Comput 44(5):647–659

Day K, Al-Ayyoub AE (1997) Fault diameter of k-ary n-cube networks. IEEE Trans Parallel Distrib Syst 8(9):903–907

Diks K, Pele A (1996) Efficient gossiping by packets in networks with random faults. SIAM J Discrete Math 9(1):7–18

Efe K (1992) The crossed cube architecture for parallel computation. IEEE Trans Parallel Distrib Syst 3(5):513–524

Esfahanian AH, Hakimi SL (1958) Fault-tolerant routing in de Bruijn communication networks. IEEE Trans Comput C-34(9):777–788

Fu J-S (2003) Fault-tolerant cycle embedding in the hypercube. Parallel Comput 29(6):821–832

Fu J-S (2006) Conditional fault-tolerant Hamiltonicity of twisted cubes. In: Proceedings of 7th parallel and distributed computing, applications and technologies (PDCAT’06). IEEE Comput Soc, Los Alamitos, pp 5–10

Fu J-S (2007) Conditional fault-tolerant Hamiltonicity of star graphs. Parallel Comput 33:488–496

Hilbers PAJ, Koopman MRJ, van de Snepscheut JLA (1987) The twisted cube. In: Proceedings of the conference on parallel architectures and languages Europe, vol I: Parallel architectures. Lecture notes in computer science, vol 258, pp 152–159

Hillis DW (1982) The connection machine. MIT Press, Cambridge

Hsieh SY (2005) Embedding longest fault-free paths onto star graphs with more vertex faults. Theor Comput Sci 337(1–3):370–378

Hsieh SY (2006) Fault-Tolerant cycle embedding in the hypercube with more both faulty vertices and faulty edges. Parallel Comput 32(1):84–91

Hsieh SY, Wu CD (2007) Conditional edge-fault-tolerant Hamiltonian cycle embedding of star graphs. In: Proceedings of the 13th international conference on parallel and distributed systems (ICPADS’07). IEEE Comput Soc, Los Alamitos

Hsieh SY, Ho CW, Chen GH (1999) Fault-free Hamiltonian cycles in faulty arrangement graphs. IEEE Trans Parallel Distrib Syst 10(3):223–237

Hsieh SY, Chen GH, Ho CW (2001a) Longest fault-free paths in star graphs with vertex faults. Theor Comput Sci 262(1–2):215–227

Hsieh SY, Chen GH, Ho CW (2001b) Longest fault-free paths in star graphs with edge faults. IEEE Trans Comput 50(9):960–971

Hung HS, Chen GH, Fu JS (2007) Fault-free Hamiltonian cycles in crossed cubes with conditional link faults. Inf Sci 177(24):5664–5674

Leighton FT (1992) Introduction to parallel algorithms and architecture: arrays, trees, hypercubes. Morgan Kaufmann, San Mateo

Liang AC, Bhattacharya S, Tsai WT (1994) Fault-tolerant multicasting on hypercubes. J Parallel Distrib Comput 23:418–428

Parhami B (1999) Introduction to parallel processing: algorithms and architectures. Plenum, New York

Park JH, Kim HC, Lim HS (2005) Fault-Hamiltonicity of hypercube-like interconnection networks. In: Proceedings of the 19th IEEE International parallel and distributed processing symposium, 2005 (IPDPS’05), vol 1, pp 60.1

Singhvi N, Ghose K (1995) The Mcube: a symmetrical cube based network with twisted links. In: Proceedings of the 9th international symposium of parallel processing, Honolulu, pp 11–16

Tsai CH (2004) Linear array and ring embeddings in conditional faulty hypercubes. Theor Comput Sci 314:431–443

Tseng YC, Chang SH, Sheu JP (1997) Fault-tolerant ring embedding in a star graph with both link and node failures. IEEE Trans Parallel Distrib Syst 8(12):1185–1195

Wang NC, Chu CP, Chen TS (2002) A dual-Hamiltonian-path-based multicasting strategy for wormhole-routed star graph interconnection networks. J Parallel Distrib Comput 62(12):1747–1762

Wang NC, Yen CP, Chu CP (2005) Multicast communication in wormhole-routed symmetric networks with Hamiltonian cycle model. J Syst Archit 51(3):165–183

Wu J (1995) Safety levels—an efficient mechanism for achieving reliable broadcasting in hypercubes. IEEE Trans Comput 44(5):702–706

Yang PJ, Tien SB, Raghavendra CS (1994) Embedding of rings and meshes onto faulty hypercubes using free dimensions. IEEE Trans Comput 43(5):608–613

Yang XF, Evans DJ, Megson GM (2005) The locally twisted cubes. Int J Comput Math 82(4):401–413