The t/m-diagnosis strategy of augmented k-ary n-cubes

Abstract

As the scale of interconnected networks grows, so does the number of processor failures in the network. When a processor fails, the information transmitted through the failed processor is unreliable. In fact, the higher the network's diagnosability, the more reliable it is. The t/m-diagnosis strategy was proposed [20], the primary principle of which is to sacrifice less diagnostic accuracy to massively improve the diagnosability, with the goal of enhancing the reliability of the network. This paper presents the t/m-diagnosis algorithm and shows the t/m-diagnosability of the augmented k-ary n-cube AQn,k, which is an extension of k-ary n-cubes and augmented cubes. In detail, we show that AQn,k is [4n(1+m)−⌊5(1+m)22⌋]/m-diagnosable under the PMC model (n≥4, k≥4 and 0≤m≤n−2) and under the MM* model (n≥4, k≥4 and 1≤m≤n−2), respectively. Based on these results, we further propose the polynomial-time t/m-diagnosis algorithm on the node number of AQn,k under the PMC and MM* models respectively.