A general technique to establish the asymptotic conditional diagnosability of interconnection networks

Abstract

We develop a general and demonstrably widely applicable technique for determining the asymptotic conditional diagnosability of interconnection networks prevalent within parallel computing under the comparison diagnosis model. We apply our technique to replicate (yet extend) existing results for hypercubes and k-ary n-cubes before going on to obtain new results as regards folded hypercubes, pancake graphs and augmented cubes. In particular, we show that the asymptotic conditional diagnosability of: folded hypercubes {FQn} is 3n−2, pancake graphs {Pn} is 3n−7, and augmented cubes {AQn} is 6n−17. We demonstrate how our technique is independent of structural properties of the interconnection network G in question and essentially only dependent upon the minimal size of the neighbourhood of a path of length 2 in G, the number of neighbours any two distinct vertices of G have in common, and the minimal degree of any vertex in G.