Connectivity in large-scale data center networks is a critical indicator to evaluate network state. A feasible and performance-guaranteed algorithm enables us to find disjoint paths between network vertices to ensure effective data transfer and to maintain the normal operation of network in case of faulty 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 propose a vertex disjoint path algorithm with the time complexity of O(nk) in BCCC, where n denotes a switch connected to n servers and k denotes dimension. Then, we prove that the restricted connectivity of BCCC(n,k). Finally, we present an O(knκ1(G)) fault-free algorithm in BCCC, where κ1(G) is the restricted connectivity. This algorithm can obtain a fault-free path between any two distinct fault-free vertices under the condition that each vertex has at least one fault-free neighbor in the BCCC and a set of faulty vertices F with |F|<κ1(G).

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.

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