Research on the 2-Good-Neighbor Conditional Diagnosability of Augmented Cubes

Diagnosability is an important metric measuring the reliability of multiprocessor system. The classical problem of fault diagnosis is discussed widely and the diagnosability of many well-know networks have been further explored. Fault diagnosis of the system restrains that every free-fault nodes has at least g free-fault neighbor vertices, which is called the g-good-neighbor conditional diagnosis. As a famous topology structure of interconnection networks, the n-dimensional augmented cubes have many good properties. By analyzing and demonstrating the properties of 2-good-neighbor conditional diagnosis for augmented cubes, this paper first proves that the 2-good-neighbor conditional diagnosability of augmented cubes under the MM* model is 8n-18. The result shows that the 2-good-neighbor conditional diagnosability of augmented cubes is larger than its classical diagnosability 2n-1.

[1]  P. Cull,et al.  The Mobius Cubes , 1991, The Sixth Distributed Memory Computing Conference, 1991. Proceedings.

[2]  Samuel C. Lee,et al.  Logic and Computer Design in Nanospace , 2008, IEEE Transactions on Computers.

[3]  Sun-Yuan Hsieh,et al.  Conditional Diagnosability of Augmented Cubes under the PMC Model , 2012, IEEE Transactions on Dependable and Secure Computing.

[4]  Tsung-Yen Chuang,et al.  The Strong Diagnosability of Regular Networks and Product Networks under the PMC Model , 2009, IEEE Trans. Parallel Distributed Syst..

[5]  Cheng-Kuan Lin,et al.  The g-good-neighbor conditional diagnosability of hypercube under PMC model , 2012, Appl. Math. Comput..

[6]  Jimmy J. M. Tan,et al.  Conditional diagnosability measures for large multiprocessor systems , 2005, IEEE Transactions on Computers.

[7]  Miroslaw Malek,et al.  A comparison connection assignment for diagnosis of multiprocessor systems , 1980, ISCA '80.

[8]  Shuming Zhou,et al.  The g-good-neighbor diagnosability of (n, k)-star graphs , 2017, Theor. Comput. Sci..

[9]  Sun-Yuan Hsieh,et al.  Diagnosability of Two-Matching Composition Networks , 2008, COCOON.

[10]  Liang-Cheng Ye,et al.  Five-Round Adaptive Diagnosis in Hamiltonian Networks , 2015, IEEE Transactions on Parallel and Distributed Systems.

[11]  Jun-Ming Xu,et al.  The super connectivity of augmented cubes , 2008, Inf. Process. Lett..

[12]  Deyu Qi,et al.  The twisted crossed cube , 2016, Concurr. Comput. Pract. Exp..

[13]  Shuming Zhou,et al.  Diagnosabilities of regular networks under three-valued comparison models , 2017, Int. J. High Perform. Comput. Netw..

[14]  Kemal Efe.  A Variation on the Hypercube with Lower Diameter , 1991, IEEE Trans. Computers.

[15]  Li Xu,et al.  The g-Good-Neighbor Conditional Diagnosability of Arrangement Graphs , 2016, IEEE Trans. Dependable Secur. Comput..

[16]  Xiao Qin,et al.  The ${\schmi g}$-Good-Neighbor Conditional Diagnosability of ${\schmi k}$-Ary ${\schmi n}$-Cubes under the PMC Modeland MM* Model , 2015, IEEE Transactions on Parallel and Distributed Systems.

[17]  Shiying Wang,et al.  The 1-good-neighbour diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model , 2016, Int. J. Comput. Math..

[18]  Abhijit Sengupta,et al.  On self-diagnosable multiprocessor systems: diagnosis by the comparison approach , 1989, [1989] The Nineteenth International Symposium on Fault-Tolerant Computing. Digest of Papers.

[19]  Liang-Cheng Ye,et al.  A Fast Pessimistic Diagnosis Algorithm for Hypercube-Like Networks under the Comparison Model , 2016, IEEE Transactions on Computers.

[20]  GERNOT METZE,et al.  On the Connection Assignment Problem of Diagnosable Systems , 1967, IEEE Trans. Electron. Comput..

[21]  Sun-Yuan Hsieh,et al.  Strongly Diagnosable Product Networks Under the Comparison Diagnosis Model , 2008, IEEE Transactions on Computers.

[22]  Shiying Wang,et al.  The g-good-neighbor conditional diagnosability of n-dimensional hypercubes under the MM⁎ model , 2016, Inf. Process. Lett..

[23]  Zhenhua Wang,et al.  The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks , 2017, Discret. Appl. Math..