Hamiltonian Properties of DCell Networks

TL;DR

This paper proves Hamiltonian properties of DCell networks, demonstrating their connectivity, fault tolerance, and providing algorithms for Hamiltonian path finding, which are crucial for efficient data center network design.

Contribution

The paper establishes Hamiltonian-connectedness and fault tolerance of DCell networks and introduces an efficient algorithm for Hamiltonian path discovery.

Findings

DCell is Hamiltonian-connected for all levels with certain conditions.

An $O(t_k)$ algorithm for finding Hamiltonian paths in DCell.

DCell networks are fault-tolerant and maintain Hamiltonian properties under failures.

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 $k \geq 0$ and $n \geq 2$. Our proof extends to all generalized DCell connection rules for $n\ge 3$. 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.