The g-extra conditional diagnosability and sequential t/k-diagnosability of hypercubes

• Published in: International journal of computer mathematics Vol. 93; no. 3; pp. 482 - 497
• Main Authors: Zhang, Shurong, Yang, Weihua
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.03.2016; Taylor & Francis Ltd
• Subjects: Algorithms; Computer simulation; conditional diagnosability; Diagnosis; diagnosis algorithms; Fault diagnosis; Fault tolerance; Hypercubes; Mathematical models; Strategy; system-level diagnosis
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2015.1020796

The conditional diagnosis is a very important measure of the reliability and the fault-tolerance of networks. The 'condition' means that no faulty set contains all neighbours of any node. Under this assumption, for any system G, every component of has more than 1 node, where F is the faulty set of G. The g-extra conditional diagnosability is defined under the assumption that every component of has more than nodes. 'A system with at most t faulty nodes is defined as sequentially t-diagnosable if at least one faulty node can be repaired, so that the testing can be continued using the repaired node to eventually diagnose all faulty nodes' [E.P. Duarte Jr., R.P. Ziwich, and L.C.P. Albini, A survey of comparison-based system-level diagnosis, ACM Comput. Surv. 43(3) (2011), article 22]. To increase the degree of the sequential t-diagnosability of a system, sequential -diagnosis strategy is proposed in this paper. It is allowed that there are at most k misdiagnosed nodes. In this paper, we determine the g-extra conditional diagnosability of hypercubes and propose sequential -diagnosis algorithms for hypercubes with low time complexities under the Preparata, Metze, and Chien (PMC) model and the MM* model which is a special case of the Maeng and Malek (MM) model.