Fault-Tolerant and Unicast Performances of the Data Center Network HSDC

In order to satisfy the rapidly increasing demand for data volume, large data center networks (DCNs) have been proposed. In 2019, Zhang et al. proposed a new highly scalable DCN architecture named HSDC (Highly Scalable Data Center Network), which can achieve greater incremental scalability. In this paper, we give the definition of the logical graph of HSDC, named $$H_n$$ , which can be treated as a compound graph of hypercube and complete graph of the same dimension. First, we prove that the connectivity and tightly super connectivity of $$H_n$$ are both n. Then, we give an O(n) shortest unicast algorithm to find a shortest path between any two distinct nodes in $$H_n$$ , and prove the correctness of this algorithm. In fact, we also prove that the  length of the shortest path constructed by this algorithm is no more than $$2d+1$$ if $$d<n$$ and at most 2d if $$d=n$$ , where d is the Hamming distance between  the start and end nodes, and the diameter of $$H_n$$ is 2n.