Abstract
A set of <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> spanning trees in a graph <inline-formula><tex-math notation="LaTeX">$G$</tex-math></inline-formula> are called completely independent spanning trees (CISTs for short) if the paths joining every pair of vertices <inline-formula><tex-math notation="LaTeX">$x$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$y$</tex-math></inline-formula> in any two trees have neither vertex nor edge in common, except for <inline-formula><tex-math notation="LaTeX">$x$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$y$</tex-math></inline-formula> . The existence of multiple CISTs in the underlying graph of a network has applications in fault-tolerant broadcasting and secure message distribution. In this paper, we investigate the construction of CISTs in a server-centric data center network called BCube connected crossbars (BCCC), which can provide good network performance using inexpensive commodity off-the-shelf switches and commodity servers with only two network interface card (NIC) ports. The significant advantages of BCCC are its good expandability, lower communication latency, and higher robustness in component failure. Based on the structure of compound graphs of BCCC, we provide efficient algorithms to construct <inline-formula><tex-math notation="LaTeX">$\lceil \frac{n}{4}\rceil$</tex-math></inline-formula> CISTs in the logical graph of BCCC, denoted by <inline-formula><tex-math notation="LaTeX">$L$</tex-math></inline-formula> - <inline-formula><tex-math notation="LaTeX">$BCCC(n,k)$</tex-math></inline-formula> , for <inline-formula><tex-math notation="LaTeX">$n\geqslant 5$</tex-math></inline-formula> . As a by-product, we obtain a fault-tolerant routing that takes the constructed CISTs as its routing table. We then evaluate the performance of the fault-tolerant routing through simulation results.
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