Hamiltonian Properties of DCell Networks

Abstract

Abstract. 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 . What's more, 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.

Fault-Tolerant Secure Routing of B H n -Based Data Center Networks

“…Wang et al [22] proposed an efficient algorithm for finding a disjoint paths in the node-to-set routing of DCell networks. Subsequently, they studied the Hamiltonian properties of DCell networks and extend it to all generalized DCell Hamiltonian-connected [23], the restricted h-connectivity [24], and vertexdisjoint paths in DCell networks successively [25]. Li et al [6] studied the diagnosability and g-good-neighbor conditional diagnosability of the data center network DCell.…”

The influence of datacenter usage on symmetry in datacenter network design

“…It was proved in [25] that any WK-recursive network of amplitude at least 4 is Hamiltonian-connected; consequently, HCN is Hamiltonian-connected (when all switch-nodes have degree at least 4). It was shown in [57] that (apart from a very small number of cases) DCell is Hamiltonianconnected and remains Hamiltonian-connected even in the presence of (a limited number of) faults. The fact that DCell is strongly completely connected means that it has numerous useful cycles embedded, with the Hamiltonian connectedness adding to the flexibility of finding these cycles (it should be added that an algorithm to find a Hamiltonian path in DCell is given in [57]).…”

“…It was shown in [57] that (apart from a very small number of cases) DCell is Hamiltonianconnected and remains Hamiltonian-connected even in the presence of (a limited number of) faults. The fact that DCell is strongly completely connected means that it has numerous useful cycles embedded, with the Hamiltonian connectedness adding to the flexibility of finding these cycles (it should be added that an algorithm to find a Hamiltonian path in DCell is given in [57]). As was remarked in [57], the constructions used there do not apply to FiConn and do not yield pancyclicity results for DCell.…”

“…The fact that DCell is strongly completely connected means that it has numerous useful cycles embedded, with the Hamiltonian connectedness adding to the flexibility of finding these cycles (it should be added that an algorithm to find a Hamiltonian path in DCell is given in [57]). As was remarked in [57], the constructions used there do not apply to FiConn and do not yield pancyclicity results for DCell. The clique-abstraction of the DCN BCube is the generalized hypercube.…”

“…Of course, this should be combined with extensive simulations of the DCNs under new virtualization methodologies and also under many-to-may traffic patterns (and indeed other traffic patterns arising through datacenter usage). A start has been made in, for example, [57]. As regards simulation, we have developed an opensource, flow-based simulator INRFlow [20] that is specifically designed for flow-based simulation in server-centric DCNs and which can be extended in order to perform these simulations.…”