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The \(g\)-good-neighbor conditional diagnosabilities of hypermesh optical interconnection networks under the PMC and comparison models. (English) Zbl 07837625

Summary: Processor fault diagnosis is intended to identify faulty processors of a multicomputer system, guaranteeing its high reliability and availability. The \(g\)-good-neighbor conditional diagnosability is a novel fault diagnosis method for various networks. Under the PMC model and comparison model, the \(g\)-good-neighbor conditional diagnosabilities of hypermesh optical interconnection networks are determined, respectively. Directly applying the results, the \(g\)-good-neighbor conditional diagnosabilities of hypercubes are derived under the PMC and comparison models.

MSC:

68Mxx Computer system organization
68Rxx Discrete mathematics in relation to computer science
05Cxx Graph theory
Full Text: DOI

References:

[1] Bondy, J. A. and Murty, U. S. R., Graph Theory, Springer, New York, 2008. · Zbl 1134.05001
[2] Chang, N. W., Lin, T. Y. and Hsieh, S. Y., Conditional diagnosability of \(k\)-ary \(n\)-cubes under the PMC Model, ACM Trans. Design Automation of Electronic Systems17 (2012), Article 46.
[3] Cheng, E., Qiu, K. and Shen, Z., On the conditional diagnosability of matching composition networks, Theoret. Comput. Sci.557 (6)(2014) 101-114. · Zbl 1338.68028
[4] Cheng, E., Qiu, K. and Shen, Z., A general approach to deriving the \(g\)-good-neighbor conditional diagnosability of interconnection networks, Theoret. Comput. Sci.757(24) (2019) 56-67. · Zbl 1410.68060
[5] Fan, J., Diagnosability of crossed cubes under the comparison diagnosis model, IEEE Trans. Parallel Distrib. Syst.13(7) (2002) 687-692.
[6] Guo, J., Li, D. and Lu, M., The \(g\)-good-neighbor conditional diagnosability of the crossed cubes under the PMC and MM* model, Theoret. Comput. Sci.75510 (2019) 81-88. · Zbl 1411.68023
[7] Hsieh, S. Y., Tsai, C. Y. and Chen, C. A., Strong diagnosability and conditional diagnosability of multiprocessor systems and folded hypercubes, IEEE Trans. Comput.62 (2013) 1472-1477. · Zbl 1365.94699
[8] Lai, P. L., Tan, J. J. M., Chang, C. P. and Hsu, L. H., Conditional diagnosability measures for large multiprocessor systems, IEEE Trans. Comput.54 (2005) 165-175.
[9] Li, X., Yang, X. and He, L., Diagnosability of optical multi-mesh hypercube networks under the comparison diagnosis model, Int. J. Comput. Math.90(9) (2013) 1774-1781. · Zbl 1312.68027
[10] Li, X., Strong diagnosability and conditional diagnosability of optical multi-mesh hypercube networks under the PMC model, Int. J. Comput. Math.93(12) (2016) 2054-2063. · Zbl 1404.68026
[11] Li, X., Yang, X., He, L., Yu, C. and Zhang, J., Conditional fault tolerance of hypermesh optical interconnection networks, Int. J. Found. Comput. S.26(1) (2015) 159-168. · Zbl 1312.68028
[12] Li, X., Yang, X., He, L., Zhang, J. and Yu, C., Conditional diagnosability of optical multi-mesh hypercube networks under the comparison diagnosis model, Theoret. Comput. Sci.531 (2014) 47-53. · Zbl 1359.68029
[13] Li, D. and Lu, M., The \(g\)-good-neighbor conditional diagnosability of star graphs under the PMC and MM* model, Theoret. Comput. Sci.674 (2017) 53-59. · Zbl 1370.68034
[14] Li, X. Y., Fan, J. X., Lin, C.-K and Jia, X. H., Diagnosability evaluation of the data center network DCell, Comput. J.61(1) (2018) 129-143.
[15] Liu, H., Hu, X. and Gao, S., The \(g\)-good-neighbor conditional diagnosability of twisted hypercubes under the PMC and MM* model, Appl. Math. Comput.3321 (2018) 484-492. · Zbl 1427.05185
[16] Liu, X., Yang, X. and Xiang, M., One-step \(t\)-fault diagnosis for hypermesh optical interconnection multiprocessor systems, J. Syst. Softw.82 (2009) 1491-1496.
[17] Loucif, S., Ould-Khaoua, M. and Al-Ayyoub, A., Hypermeshes: Implementation and performance, J. Syst. Architect.48 (2002) 37-47.
[18] Maeng, J. and Malek, M., A comparison connection assignment for self-diagnosis of multiprocessors systems, Proc. \(11\) th Int. Symp. Fault-Tolerant Comput. Los Alamitos, CA, USA, , 1981, 173-175.
[19] Malek, M., A comparison connection assignment for diagnosis of multiprocessor systems, Proc. Seventh Int. Symp. Computer Architecture, La Baule, France, , 1980, 31-36.
[20] Moraveji, R., Sarbazi-Azad, H., Nayebi, A. and Navi, K., Modeling the effects of hot-spot traffic load on the performance of wormhole-switched hypermeshes, Comput. Electr. Engin.37 (2011) 1-23. · Zbl 1214.68103
[21] Peng, S. L., Lin, C. K., Tan, J. J. M. and Hsu, L. H., The \(g\)-good-neighbor conditional diagnosability of hypercube under PMC model, Appl. Math. Comput.218 (2012) 10406-10412. · Zbl 1247.68032
[22] Preparata, F. P., Metze, G. and Chien, R. T., On the connection assignment problem of diagnosable systems, IEEE Trans. Electron. Comput.16 (1967) 848-854. · Zbl 0189.16904
[23] Ren, Y. X. and Wang, S. Y., The \(g\)-good-neighbor diagnosability of locally twisted cube, Theoret. Comput. Sci.697 (2017) 91-97. · Zbl 1379.68024
[24] Sengupta, A. and Dahbura, A. T., On self-diagnosable multiprocessor systems: Diagnosis by the comparison approach, IEEE Trans. Comput.41 (1992) 1386-1396. · Zbl 1395.68062
[25] Tsai, C. H. and Chen, J. C., Fault isolation and identification in general biswapped networks under the PMC diagnostic model, Theoret. Comput. Sci.501 (2013) 62-71. · Zbl 1296.68020
[26] Wang, S. and Han, W., The \(g\)-good-neighbor conditional diagnosability of \(n\)-dimensional hypercubes under the MM* model, Inf. Process. Lett.116 (2016) 574-577. · Zbl 1357.68016
[27] Wang, M., Lin, Y. and Wang, S., The 2-good-neighbor diagnosability of Cayley graphs generated by transposition trees under the PMC model and MM* model, Theoret. Comput. Sci.628 (2016) 92-100. · Zbl 1338.68036
[28] Wang, S. Y. and Wang, Z. H., \(g\)-good-neighbor conditional diagnosability of star graph networks under PMC model and MM* model, Front. Math. China12(5) (2017) 1221-1234. · Zbl 1378.05194
[29] Wang, S. and Wang, M., The \(g\)-good neighbor and \(g\)-extra diagnosability of networks, Theoret. Comput. Sci.773 (2019) 107-114. · Zbl 1422.68013
[30] Wei, Y. L. and Xu, M., On \(g\)-good-neighbor conditional diagnosability of \((n,k)\)-star networks, Theoret. Comput. Sci.697 (2017) 79-90. · Zbl 1379.68025
[31] Wu, J. and Guo, G., Fault tolerance measures for \(m\)-ary \(n\)-dimensional hypercubes based in forbidden faulty sets, IEEE Trans. Comput.47 (1998) 888-893. · Zbl 0894.68001
[32] Xu, X., Li, X. W., Zhou, S. M., Hao, R. X. and Gu, M. M., The \(g\)-good-neighbor diagnosability of \((n,k)\)-star graphs, Theoret. Comput. Sci.659 (2017) 53-63. · Zbl 1355.68027
[33] Yang, E., Yang, X., Dong, Q. and Li, J., Conditional diagnosability of hypermesh optical multiprocessor systems under the PMC model, Int. J. Comput. Math.88 (2011) 2275-2284. · Zbl 1230.68047
[34] Yang, E., Yang, X., Dong, Q. and Li, J., Conditional diagnosability of hypermeshes under the comparison model, Inf. Process. Lett.111 (2011) 188-193. · Zbl 1260.68026
[35] Yuan, J., Liu, A., Qin, X., Zhang, J. and Li, J., \(g\)-Good-neighbor conditional diagnosability measures for 3-ary \(n\)-cube networks, Theoret. Comput. Sci.626 (2016) 144-162. · Zbl 1336.68018
[36] Yuan, J., Liu, A., Ma, X., Liu, X., Qin, X. and Zhang, J., The \(g\)-good-neighbor conditional diagnosability of \(k\)-ary \(n\)-cubes under the PMC model and MM* model, IEEE Trans. Parallel Distrib. Syst.26 (2015) 1165-1177.
[37] Zhou, M., Li, Y., Tahir, M. J., Gong, X., Wang, Y. and He, W., Integrated statistical test of signal distributions and access point contributions for Wi-Fi indoor localization, IEEE Trans. on Veh. Technol.70(5) (2021) 5057-5070.
[38] Zhou, S., Song, S., Yang, X. and Chen, L., On conditional fault tolerance and diagnosability of hierarchical cubic networks, Theoret. Comput. Sci.609 (2016) 421-433. · Zbl 1331.68035
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