Constructing Completely Independent Spanning Trees in a Family of Line-Graph-Based Data Center Networks
Yifeng Wang, Baolei Cheng, Qian Yu, Dajin Wang
Abstract
The past decade has seen growing importance being attached to the <i>Completely Independent Spanning Trees</i> (CISTs). The CISTs can facilitate many network functionalities, and the existence and construction schemes of CISTs in various networks can be an indicator of the network's robustness. In this paper, we establish the number of CISTs that can be constructed in the <i>line graph</i> of the complete graph <inline-formula><tex-math notation="LaTeX">$K_n$</tex-math></inline-formula> (denoted <inline-formula><tex-math notation="LaTeX">$L(K_n)$</tex-math></inline-formula> , for <inline-formula><tex-math notation="LaTeX">$n\geq 4$</tex-math></inline-formula> ), and present an algorithm to construct the optimal (i.e., maximal) number of CISTs in <inline-formula><tex-math notation="LaTeX">$L(K_n)$</tex-math></inline-formula> . The <inline-formula><tex-math notation="LaTeX">$L(K_n)$</tex-math></inline-formula> is a special class of SWCube [13], an architectural model proposed for data center networks. Our construction algorithm is also implemented to verify its validity.