Issue No. 05 - May (2007 vol. 18)

ISSN: 1045-9219

pp: 598-607

ABSTRACT

<p><b>Abstract</b>—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 <tmath>t{\hbox{-}}{\rm diagnosable}</tmath>. 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 <tmath>G(V,E)</tmath> 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 <tmath>n{\hbox{-}}{\rm dimensional}</tmath> hypercube <tmath>Q_{n}</tmath> has this strong property, <tmath>n \geq 3</tmath>. Next, we study the local diagnosability of a faulty hypercube. We prove that <tmath>Q_{n}</tmath> keeps this strong property even if it has up to <tmath>n - 2</tmath> faulty edges. Assuming that each vertex of a faulty hypercube <tmath>Q_{n}</tmath> is incident with at least two fault-free edges, we prove <tmath>Q_{n}</tmath> keeps this strong property even if it has up to <tmath>3(n - 2) - 1</tmath> faulty edges. Furthermore, we prove that <tmath>Q_{n}</tmath> keeps this strong property no matter how many edges are faulty, provided that each vertex of a faulty hypercube <tmath>Q_{n}</tmath> is incident with at least three fault-free edges. Our bounds on the number of faulty edges are all tight.</p>

INDEX TERMS

PMC model, local diagnosability, strong local diagnosability property.

CITATION

Jimmy J.M. Tan, Guo-Huang Hsu, "A Local Diagnosability Measure for Multiprocessor Systems",

*IEEE Transactions on Parallel & Distributed Systems*, vol. 18, no. , pp. 598-607, May 2007, doi:10.1109/TPDS.2007.1022