Hamiltonian Properties of DCell Networks

DCell has been proposed for data centers as a server centric interconnection network structure. DCell can support millions of servers with high network capacity by only using commodity switches. With one exception, we prove that a k level DCell built with n port switches is Hamiltonian-connected for k ≥ 0 and n ≥ 2. Our proof extends to all generalized DCell connection rules for n ≥ 3. Then, we propose an O(tk) algorithm for finding a Hamiltonian path in DCellk, where tk is the number of servers in DCellk. What’s more, we prove that DCellk is (n + k − 4)-fault Hamiltonian-connected and (n + k − 3)-fault Hamiltonian. In addition, we show that a partial DCell is Hamiltonian connected if it conforms to a few practical restrictions.