Fault-tolerant cycle embedding in the hypercube

Almost all the previous fault-tolerant cycle embedding research could not tolerate the faulty nodes more than the degree of the network. In this paper, we have broken this limitation: a recursive method of embedding a longest cycle into an n-dimensional hypercube (n-cube), which can tolerate atmost 2n- 4 faulty nodes, is proposed. The best result thus far is to tolerate only atmost n - 1 faulty nodes, which is less than the degree of the n-cube.

[1]  Frank Thomson Leighton.  Introduction to parallel algorithms and architectures: arrays , 1992 .

[2]  John P. Hayes,et al.  Edge fault tolerance in graphs , 1993, Networks.

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

[4]  Gen-Huey Chen,et al.  Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs , 1999, IEEE Trans. Parallel Distributed Syst..

[5]  Frank Harary,et al.  Distance in graphs , 1990 .

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

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

[8]  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.

[9]  Bella Bose,et al.  Fault-Tolerant Ring Embedding in de Bruijn Networks , 1993, IEEE Trans. Computers.

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

[11]  Arkady Kanevsky,et al.  Embedding rings in recursive networks , 1994, Proceedings of 1994 6th IEEE Symposium on Parallel and Distributed Processing.

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

[13]  Gen-Huey Chen,et al.  Embed longest rings onto star graphs with vertex faults , 1998, Proceedings. 1998 International Conference on Parallel Processing (Cat. No.98EX205).

[14]  Dajin Wang.  Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links , 2001, J. Parallel Distributed Comput..

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

[16]  Bella Bose,et al.  Distributed Ring Embedding in Faulty De Bruijn Networks , 1997, IEEE Trans. Computers.

[17]  Yu-Chee Tseng,et al.  Fault-Tolerant Ring Embedding in a Star Graph with Both Link and Node Failures , 1997, IEEE Trans. Parallel Distributed Syst..