Title :
Conditional Diagnosability of Matching Composition Networks Under the PMC Model
Author :
Xu, Min ; Thulasiraman, Krishnaiyan ; Hu, Xiao-Dong
Author_Institution :
Lab. of Math. & Complex Syst., Beijing Normal Univ., Beijing, China
Abstract :
In the work of Lai in 2005, they proposed a new measure for fault diagnosis of systems, namely, conditional diagnosability. It assumes that no fault set can contain all the neighbors of any vertex in the system. In the same paper, they showed that the conditional diagnosability of hypercube Qn is 4(n - 2) + 1 for n ges 5. In this brief, we generalize this result by considering a family of more popular networks, namely, matching composition networks (MCNs), which are a class of networks composed of two components of the same order linked by a perfect matching under PMC (Preparata, Metze and Chien) model. We determine in Theorem 7 the conditional diagnosability for some MCNs, from which we deduce that the hypercube Qn, the crossed cube CQn, the twisted cube TQn, and the MOumlbius cube MQn all have the same conditional diagnosability of 4(n - 2) + 1 for n ges 5. We show that the bijective connection (BC) networks in the work of Fan and He in 2003 and the work of Zhu in 2008 satisfy the conditions of Theorem 7, and thus, our conditional diagnosability result also applies to BC networks. Finally, we show that the MCNs satisfying the conditions of Theorem 7 are more general than the BC networks.
Keywords :
fault diagnosis; graph theory; hypercube networks; network theory (graphs); set theory; BC network; MCN; Mobius cube network; PMC model; Preparata-Metze-and-Chien model; bijective connection network; conditional diagnosability; crossed cube network; fault diagnosis; faulty vertex set; graph theory; hypercube network; matching composition network; twisted cube network; Conditional diagnosability; PMC model; conditional faulty set; diagnosability;
Journal_Title :
Circuits and Systems II: Express Briefs, IEEE Transactions on
DOI :
10.1109/TCSII.2009.2030361