The t/k-Diagnosability and a t/k Diagnosis Algorithm of the Data Center Network BCCC under the MM* Model

The evaluation of the fault diagnosis capability of a data center network (DCN) is important research in measuring network reliability. The g-extra diagnosability is defined under the condition that every component except the fault vertex set contains at least g+1 vertices. The t/k diagnosis strategy is that the number of fault nodes does not exceed t, and all fault nodes can be isolated into a set containing up to k fault-free nodes. As an important data center network, BCube Connected Crossbars (BCCC) has many excellent properties that have been widely studied. In this paper, we first determine that the g-extra connectivity of BCn,k for 0≤g≤n−1. Based on this, we establish the g-extra conditional diagnosability of BCn,k under the MM* model for 1≤g≤n−1. Next, based on the conclusion of the largest connected component in g-extra connectivity, we prove that the t/k-diagnosability of BCn,k under the MM* model for 1≤k≤n−1. Finally, we present a t/k diagnosis algorithm on BCCC under the MM* model. The algorithm can correctly identify all nodes at most k nodes undiagnosed. So far, t/k-diagnosability and diagnosis algorithms for most networks in the MM* model have not been studied.