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(t(k)) algorithm for finding a Hamiltonian path in DCell(k), where t(k) is the number of servers in DCell(k). Furthermore, we prove that DCell(k) 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.