AAM  >> Vol. 5 No. 2 (May 2016)

    交叉立方体的1好邻连通度和诊断度
    The 1-Good-Neighbor Connectivity and Diagnosability of Crossed Cubes

  • 全文下载: PDF(567KB) HTML   XML   PP.282-290   DOI: 10.12677/AAM.2016.52036  
  • 下载量: 291  浏览量: 761   国家自然科学基金支持

作者:  

马晓蕾,王贞化:河南师范大学,数学与信息科学学院,河南 新乡;
王世英:河南师范大学,数学与信息科学学院,河南 新乡;河南师范大学,河南省大数据统计分析与优化控制工程实验室,河南 新乡

关键词:
互连网络诊断度交叉立方体Interconnection Network Graph Diagnosability Crossed Cube

摘要:
连通度和诊断度是度量多处理器系统故障诊断能力的重要参数。2012年,Peng等提出了一个新的系统故障诊断方法,称为g好邻诊断度,它限制每个非故障顶点至少有g个非故障邻点。n维交叉立方体是超立方体的一个重要变形。本文证明了交叉立方体的1好邻连通度是2n – 2 (n ≥ 4),又证明了交叉立方体在PMC模型下的1好邻诊断度是2n – 1 (n ≥ 4)和在MM*模型下的1好邻诊断度是2n – 1 (n ≥ 5)。

Connectivity and diagnosability are important parameters in measuring the fault diagnosis of multiprocessor systems. In 2012, Peng et al. proposed a new measure for fault diagnosis of the system, which is called g-good-neighbor diagnosability that restrains every fault-free node con-taining at least g fault-free neighbors. The n-dimensional crossed cube is an important variant of the hypercube. In this paper, we prove that the 1-good-neighbor connectivity of crossed cube is 2n − 2 for n ≥ 4, and the 1-good-neighbor diagnosability of crossed cube is 2n − 1 under the PMC model for n ≥ 4 and the MM* model for n ≥ 5.

文章引用:
马晓蕾, 王世英, 王贞化. 交叉立方体的1好邻连通度和诊断度[J]. 应用数学进展, 2016, 5(2): 282-290. http://dx.doi.org/10.12677/AAM.2016.52036

参考文献

[1] Preparata, F., Metze, G. and Chien, R.T. (1968) On the Connection Assignment Problem of Diagnosable Systems. IEEE Transactions on Electronic Computers, 12, 848-854.
[2] Maeng, J. and Malek, M. (1981) A Comparison Connection Assignment for Self-Diagnosis of Multiprocessor Systems. Proceeding of 11th International Symposium on Fault-Tolerant Computing, 173-175.
[3] Lai, P.-L., Tan, J.J.M., Chang, C.-P. and Hsu, L.-H. (2005) Conditional Di-agnosability Measures for Large Multiprocessor Systems. IEEE Transactions on Computers, 54, 165-175.
http://dx.doi.org/10.1109/TC.2005.19
[4] Peng, S.-L., Lin, C.-K., Tan, J.J.M. and Hsu, L.-H. (2012) The g-Good-Neighbor Conditional Diagnosability of Hypercube under the PMC Model. Applied Mathematics Computation, 218, 10406-10412.
http://dx.doi.org/10.1016/j.amc.2012.03.092
[5] Yuan, J., Liu, A.X., Ma, X., Liu, X.L., Qin, X. and Zhang, J.F. (2015) The g-Good-Neighbor Conditional Diagnosability of k-Ary n-Cubes under the PMC Model and MM* Model. IEEE Transactions on Parallel and Distributed Systems, 26, 1165-1177.
http://dx.doi.org/10.1109/TPDS.2014.2318305
[6] Wang, M.J.S., Guo, Y.B. and Wang, S.Y. (2015) The 1-Good-Neighbor Diagnosability of Cayley Graphs Generated by Transposition Trees under the PMC Model and MM* Model. International Journal of Computer Mathematics.
[7] Bondy, J.A. and Murty, U.S.R. (2007) Graph Theory. Springer, New York.
[8] Efe, K. (1992) The Crossed Cube Architecture for Parallel Computation. IEEE Transactions on Parallel and Distributed Systems, 3, 513-524.
http://dx.doi.org/10.1109/71.159036