research-article

Component Fault Diagnosability of Hierarchical Cubic Networks

Authors:

Sun-Yuan HsiehAuthors Info & Claims

ACM Transactions on Design Automation of Electronic Systems, Volume 28, Issue 3

Article No.: 39, Pages 1 - 19

https://doi.org/10.1145/3577018

Published: 19 March 2023 Publication History

Abstract

The fault diagnosability of a network indicates the self-diagnosis ability of the network, thus it is an important measure of robustness of the network. As a neoteric feature for measuring fault diagnosability, the r-component diagnosability ct_r(G) of a network G imposes the restriction that the number of components is at least r in the remaining network of G by deleting faulty set X, which enhances the diagnosability of G. In this article, we establish the r-component diagnosability for n-dimensional hierarchical cubic network HCN_n, and we show that, under both PMC model and MM* model, the r-component diagnosability of HCN_n is rn-½(r-1)r+1 for n≥ 2 and 1≤ r≤ n-1. Moreover, we introduce the concepts of 0-PMC subgraph and 0-MM* subgraph of HCN_n. Then, we make use of 0-PMC subgraph and 0-MM* subgraph of HCN_n to design two algorithms under PMC model and MM* model, respectively, which are practical and efficient for component fault diagnosis of HCN_n. Besides, we compare the r-component diagnosability of HCN_n with the extra conditional diagnosability, diagnosability, good-neighbor diagnosability, pessimistic diagnosability, and conditional diagnosability, and we verify that the r-component diagnosability of HCN_n is higher than the other types of diagnosability.

References

[1]

John Adrian Bondy and U. S. R. Murty. 2008. Graph Theory. Springer, Berlin.

[2]

Guey-Yun Chang, Gerard J. Chang, and Gen-Huey Chen. 2005. Diagnosabilities of regular networks. IEEE Tran. Parallel Distrib. Syst. 16, 4 (2005), 341–323.

[3]

Nai-Wen Chang and Sun-Yuan Hsieh. 2018. Conditional diagnosability of \((n,k)\)-star graphs under the PMC model. IEEE Trans. Dependable Secure Comput. 15, 2 (2018), 207–216.

[4]

Saranyu Chattopadhyay, Pranesh Santikellur, Rajat Subhra Chakraborty, Jimson Mathew, and Marco Ottavi. 2021. A conditionally chaotic physically unclonable function design framework with high reliability. ACM Trans. Des. Autom. Electron. Syst. 26, 6, Article 41 (2021), 24 pages.

Digital Library

[5]

Chun-An Chen and Sun-Yuan Hsieh. 2013. \(t/t\)-Diagnosability of regular graphs under the PMC model. ACM Trans. Des. Autom. Electron. Syst. 18, 2, Article 20 (April2013), 13 pages.

Digital Library

[6]

Eddie Cheng, Ke Qiu, and Zhizhang Shen. 2015. Connectivity results of complete cubic networks as associated with linearly many faults. J. Interconnection Netw. 15, 1 & 2 (2015), 1550007 (23 pages).

[7]

Eddie Cheng, Ke Qiu, and Zhizhang Shen. 2019. A general approach to deriving the \(g\)-good-neighbor conditional diagnosability of interconnection networks. Theor. Comput. Sci. 757 (2019), 56–67.

[8]

Jianxi Fan. 2002. Diagnosability of crossed cubes under the comparison diagnosis model. IEEE Tran. Parallel Distrib. Syst. 13, 7 (2002), 687–692.

Digital Library

[9]

Kanad Ghose and Kiran R. Desai. 2002. Hierarchical cubic networks. IEEE Tran. Parallel Distrib. Syst. 6, 4 (2002), 427–435.

Digital Library

[10]

Mei-Mei Gu, Rong-Xia Hao, and Shuming Zhou. 2019. Fault diagnosability of data center networks. Theor. Comput. Sci. 776 (2019), 138–147.

Digital Library

[11]

Jia Guo, Desai Li, and Mei Lu. 2019. The \(g\)-good-neighbor conditional diagnosability of the crossed cubes under the PMC and MM* model. Theor. Comput. Sci. 755 (2019), 81–88.

[12]

Weiping Han and Shiying Wang. 2015. The \(g\)-extra conditional diagnosability of folded hypercubes. Appl. Math. Sci. 9, 146 (2015), 7247–7254.

[13]

Pao-Lien Lai, Jimmy Jiann-Mean Tan, Chien-Ping Chang, and Lih-Hsing Hsu. 2005. Conditional diagnosability measures for large multiprocessor systems. IEEE Trans. Comput. 54, 2 (2005), 165–175.

Digital Library

[14]

Chia-Wei Lee and Sun-Yuan Hsieh. 2011. Diagnosability of two-matching composition networks under the MM* model. IEEE Trans. Dependable Secure Comput. 8, 2 (2011), 246–255.

Digital Library

[15]

Xiaoyan Li, Jianxi Fan, Cheng-Kuan Lin, Baolei Cheng, and Xiaohua Jia. 2019. The extra connectivity, extra conditional diagnosability and \(t/k\)-diagnosability of the data center network DCell. Theor. Comput. Sci. 766 (2019), 16–29.

Digital Library

[16]

Limei Lin, Sun-Yuan Hsieh, Riqing Chen, Li Xu, and Chia-Wei Lee. 2018. The relationship between \(m\)-restricted connectivity and \(m\)-good-neighbor fault diagnosability of general regular networks. IEEE Trans. Rel. 67, 1 (2018), 285–296.

[17]

Limei Lin, Riqing Cheng Li Xu, Sun-Yuan Hsieh, and Dajin Wang. 2019. Relating extra connectivity and extra conditional diagnosability in regular networks. IEEE Trans. Dependable Secure Comput. 16, 6 (2019), 1086–1097.

[18]

Limei Lin, Li Xu, Dajin Wang, and Shuming Zhou. 2018. The \(g\)-good-neighbor conditional diagnosability of arrangement graphs. IEEE Trans. Dependable Secure Comput. 15, 3 (2018), 542–548.

[19]

Limei Lin, Shuming Zhou, and Li Xu. 2013. \(t/t\)-diagnosability and diagnosis algorithm on hierarchical cubic network. J. Shandong University (Natural Science) 48, 7 (2013), 85–92.

[20]

Huiqing Liu, Shunzhe Zhang, and Dong Li. 2019. On \(g\)-extra conditional diagnosability of hierarchical cubic networks. Theor. Comput. Sci. 790 (2019), 66–79.

Digital Library

[21]

Jiafei Liu, Shuming Zhou, Dajin Wang, and Hong Zhang. 2022. Component diagnosability in terms of component connectivity of hypercube-based compound networks. J. Parallel and Distrib. Comput. 162 (2022), 17–26.

Digital Library

[22]

Mengjie Lv, Shuming Zhou, Xueli Sun, Guanqin Lian, and Jiafei Liu. 2019. Reliability of \((n,k)\)-star network based on \(g\)-extra conditional fault. Theor. Comput. Sci. 757 (2019), 44–55.

[23]

Joonyoul Maeng and Miroslaw Malek. 1981. A comparison connection assignment for self-diagnosis of multiprocessors systems. In in Proc. 11th Int. Symp. Fault-Tolerant Comput.ACM Press, New York, 173–175.

[24]

Shao-Lun Peng, Cheng-Kuan Lin, Jimmy Jiann-Mean Tan, and Lih-Hsing Hsu. 2012. The \(g\)-good-neighbor conditional diagnosability of hypercube under PMC model. Appl. Math. Comput. 218 (2012), 10406–10412.

[25]

Irith Pomeranz and M. Enamul Amyeen. 2020. Logic diagnosis with hybrid fail data. ACM Trans. Des. Autom. Electron. Syst. 26, 3, Article 19 (2020), 13 pages.

[26]

Franco P. Preparata, Gernot Metze, and Robert T. Chien. 1967. On the connection assignment problem of diagnosable systems. IEEE Trans. Electron. Comput. EC-16, 6 (1967), 848–854.

[27]

Abhijit Sengupta and Anton Dahbura. 1992. On self-diagnosable multiprocessor systems: Diagnosis by the comparison approach. IEEE Trans. Comput. 41, 11 (1992), 1386–1396.

[28]

Xueli Sun, Jianxi Fan, Baolei Cheng, Zhao Liu, and Jia Yu. 2021. Component conditional fault tolerance of hierarchical folded cubic networks. Theor. Comput. Sci. 883 (2021), 44–58.

[29]

Xiang Xu, Xiaowang Li, Shuming Zhou, Rong-Xia Hao, and Mei-Mei Gu. 2017. The \(m\)-good-neighbor fault diagnosability of \((n,k)\)-star graphs. Theor. Comput. Sci. 659 (2017), 53–63.

Digital Library

[30]

Jun Yuan, Aixia Liu, Xue Ma, Xiuli Liu, Xiao Qin, and Jifu Zhang. 2015. The \(g\)-good-neighbor conditional diagnosability of \(k\)-ary \(n\)-cubes under the PMC model, and comparison model. IEEE Tran. Parallel Distrib. Syst. 26, 4 (2015), 1165–1177.

Digital Library

[31]

Shurong Zhang, Dongyue Liang, Lin Chen, Ronghua Li, and Weihua Yang. 2021. The component diagnosability of hypercubes with large-scale faulty nodes. Comput. J. 65, 5 (2022), 1129–1143.

[32]

Shurong Zhang and Weihua Yang. 2015. The \(g\)-extra diagnosability and sequential \(t/k\)-diagnosability of hypercubes. Int. J. Comput. Math. 93, 3 (2015), 482–497.

Digital Library

[33]

Shu-Li Zhao and Rong-Xia Hao. 2018. The \(g\)-good neighbour diagnosability of hierarchical cubic networks. (2018). https://arxiv.org/abs/1812.00004.

[34]

Shuming Zhou, Sulin Song, Xiaoxue Yang, and Lanxiang Chen. 2016. On conditional fault tolerance and diagnosability of hierarchical cubic networks. Theor. Comput. Sci. 609 (2016), 421–433.

Digital Library

[35]

Qiang Zhu, Xin-Ke Wang, and Guanglan Cheng. 2013. Reliability evaluation of BC networks. IEEE Trans. Comput. 62, 11 (2013), 2337–2340.

Digital Library

[36]

Hongbin Zhuang, Wenzhong Guo, Xiaoyan Li, Ximeng Liu, and Cheng-Kuan Lin. 2021. The component diagnosability of general networks. Int. J. Found. Comput. Sci. 33, 1 (2022), 67–89.

[37]

Hongbin Zhuang, Wenzhong Guo, Xiao-Yan Li, Ximeng Liu, and Cheng-Kuan Lin. 2021. The component connectivity, component diagnosability, and \(t/k\)-diagnosability of Bicube networks. Theor. Comput. Sci. 896 (2021), 145–157.

Digital Library

Cited By

Xian JXing YCai SLi WXiong XHu Z(2024)WCPNet: Jointly Predicting Wirelength, Congestion and Power for FPGA Using Multi-Task LearningACM Transactions on Design Automation of Electronic Systems10.1145/365617029:3(1-19)Online publication date: 3-May-2024
https://dl.acm.org/doi/10.1145/3656170
Feng HWu JChen L(2023)Intermittent fault diagnosability of a class of hypercube-family networks under the PMC model2023 IEEE 29th International Conference on Parallel and Distributed Systems (ICPADS)10.1109/ICPADS60453.2023.00115(757-764)Online publication date: 17-Dec-2023
https://doi.org/10.1109/ICPADS60453.2023.00115

Index Terms

Component Fault Diagnosability of Hierarchical Cubic Networks
1. Computer systems organization
  1. Dependable and fault-tolerant systems and networks
    1. Fault-tolerant network topologies
    2. Reliability
2. Networks
  1. Network properties
    1. Network reliability

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Published In

cover image ACM Transactions on Design Automation of Electronic Systems

ACM Transactions on Design Automation of Electronic Systems Volume 28, Issue 3

May 2023

456 pages

ISSN:1084-4309

EISSN:1557-7309

DOI:10.1145/3587887

Editor:
X. Sharon Hu
University of Notre Dame, USA

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Journal Family

ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 19 March 2023

Online AM: 18 January 2023

Accepted: 04 December 2022

Revised: 26 September 2022

Received: 10 September 2021

Published in TODAES Volume 28, Issue 3

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National Natural Science Foundation of China
Fok Ying Tung Education Foundation
Natural Science Foundation of Fujian Province
Fujian University of Technology

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Cited By

Xian JXing YCai SLi WXiong XHu Z(2024)WCPNet: Jointly Predicting Wirelength, Congestion and Power for FPGA Using Multi-Task LearningACM Transactions on Design Automation of Electronic Systems10.1145/365617029:3(1-19)Online publication date: 3-May-2024
https://dl.acm.org/doi/10.1145/3656170
Feng HWu JChen L(2023)Intermittent fault diagnosability of a class of hypercube-family networks under the PMC model2023 IEEE 29th International Conference on Parallel and Distributed Systems (ICPADS)10.1109/ICPADS60453.2023.00115(757-764)Online publication date: 17-Dec-2023
https://doi.org/10.1109/ICPADS60453.2023.00115

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