Longest fault-free paths in hypercubes with vertex faults

The hypercube is one of the most versatile and efficient interconnection networks (networks for short) so far discovered for parallel computation. Let f denote the number of faulty vertices in an n-cube. This study demonstrates that when f=

[1]  Chien-Ming Wang,et al.  On the fault-tolerant embeddings of complete binary trees in the mesh interconnection networks , 2002, Inf. Sci..

[2]  Abdel Elah Al-Ayyoub,et al.  Fault Diameter of k-ary n-cube Networks , 1997, IEEE Trans. Parallel Distributed Syst..

[3]  Jung-Sheng Fu.  Fault-tolerant cycle embedding in the hypercube , 2003, Parallel Comput..

[4]  Mee Yee Chan,et al.  On the Existence of Hamiltonian Circuits in Faulty Hypercubes , 1991, SIAM J. Discret. Math..

[5]  Wei-Tek Tsai,et al.  Fault-Tolerant Multicasting on Hypercubes , 1994, J. Parallel Distributed Comput..

[6]  Jimmy J. M. Tan,et al.  Hyper hamiltonian laceability on edge fault star graph , 2004, Inf. Sci..

[7]  Krzysztof Diks,et al.  Efficient Gossiping by Packets in Networks with Random Faults , 1996, SIAM J. Discret. Math..

[8]  Jimmy J. M. Tan,et al.  Fault-tolerant hamiltonian laceability of hypercubes , 2002, Inf. Process. Lett..

[9]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[10]  S. Louis Hakimi,et al.  Fault-Tolerant Routing in DeBruijn Comrnunication Networks , 1985, IEEE Transactions on Computers.

[11]  Jie Wu.  Safety Levels-An Efficient Mechanism for Achieving Reliable Broadcasting in Hypercubes , 1995, IEEE Trans. Computers.

[12]  Cauligi S. Raghavendra,et al.  Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions , 1994, IEEE Trans. Computers.

[13]  Yu-Chee Tseng.  Embedding a Ring in a Hypercube with Both Faulty Links and Faulty Nodes , 1996, Inf. Process. Lett..

[14]  Jung-Sheng Fu,et al.  Hamiltonicity of the Hierarchical Cubic Network , 2001, Theory of Computing Systems.

[15]  Norbert Ascheuer,et al.  Hamiltonian path problems in the on-line optimization of flexible manufacturing systems , 1996 .

[16]  Shahram Latifi,et al.  Optimal ring embedding in hypercubes with faulty links , 1992, [1992] Digest of Papers. FTCS-22: The Twenty-Second International Symposium on Fault-Tolerant Computing.

[17]  Selim G. Akl.  Parallel computation: models and methods , 1997 .