This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Local Diagnosability Measure for Multiprocessor Systems
May 2007 (vol. 18 no. 5)
pp. 598-607

Abstract—The problem of fault diagnosis has been discussed widely and the diagnosability of many well-known networks has been explored. Under the PMC model, we introduce a new measure of diagnosability, called local diagnosability, and derive some structures for determining whether a vertex of a system is locally t{\hbox{-}}{\rm diagnosable}. For a hypercube, we prove that the local diagnosability of each vertex is equal to its degree under the PMC model. Then, we propose a concept for system diagnosis, called the strong local diagnosability property. A system G(V,E) is said to have a strong local diagnosability property if the local diagnosability of each vertex is equal to its degree. We show that an n{\hbox{-}}{\rm dimensional} hypercube Q_{n} has this strong property, n \geq 3. Next, we study the local diagnosability of a faulty hypercube. We prove that Q_{n} keeps this strong property even if it has up to n - 2 faulty edges. Assuming that each vertex of a faulty hypercube Q_{n} is incident with at least two fault-free edges, we prove Q_{n} keeps this strong property even if it has up to 3(n - 2) - 1 faulty edges. Furthermore, we prove that Q_{n} keeps this strong property no matter how many edges are faulty, provided that each vertex of a faulty hypercube Q_{n} is incident with at least three fault-free edges. Our bounds on the number of faulty edges are all tight.

Index Terms:
PMC model, local diagnosability, strong local diagnosability property.
Citation:
Guo-Huang Hsu, Jimmy J.M. Tan, "A Local Diagnosability Measure for Multiprocessor Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 18, no. 5, pp. 598-607, May 2007, doi:10.1109/TPDS.2007.1022
Usage of this product signifies your acceptance of the Terms of Use.