The restricted hh-connectivity of the data center network DCell

Traditional data center networks (DCNs) are faced with many challenges with the development of cloud computing. This fact makes design of new DCNs represented by DCell networks become a hot research topic. For any integers k≥0k≥0 and n≥2n≥2, the kk-dimensional DCell with nn-port switches and tk,ntk,n nodes, Dk,nDk,n, has been proposed for an important DCNs as a server-centric DCN structure. In this paper, we prove that under the condition that each fault-free node of the Dk,nDk,n has at least hh fault-free neighbor(s) its restricted hh-connectivity is (h+1)(k−1)+n(h+1)(k−1)+n (resp. (n+k−h−1)th−n+1,n(n+k−h−1)th−n+1,n) with 0≤h≤n−10≤h≤n−1 (resp. n≤h≤n+k−2n≤h≤n+k−2), which is almost as (h+1)(h+1) (resp. th−n+1,nth−n+1,n) times as traditional connectivity of Dk,nDk,n. When the DCell network is used to model the topological structure of a large-scale DCN, this result can provide a more accurate measure for the fault tolerance of the network.