The pessimistic diagnosability of data center networks

A system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free processor mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by tp(G), is the maximal number of faulty processors so that the system G is t/t-diagnosable. Data centers are critical to the business of companies such as Amazon, Google, Facebook, and Microsoft. Based on data centers, the data center networks Dn,k, given in 2008, has many desirable features. In this paper, by exploring the structure of Dk,n, we firstly determined the pessimistic diagnosability of Dk,n and prove that tp(Dk,n)=n+2k−2 for k≥2 and n≥2 under the PMC model. Then we prove that Dk,n(k≥0,n≥2) is not edge transitive except the cases of k=0 and k=1,n=2.