Constructing dual-CISTs of pancake graphs and performance assessment of protection routings on some Cayley networks

Abstract

For a connected graph $G=(V,E)$, two spanning trees $T_1$ and $T_2$ of G are said to be a pair of completely independent spanning trees (or a dual-CIST for short) if for any two vertices $u,v\in V$, the paths joining u and v in the two trees have no common vertex except for u and v. Although the existence of a dual-CIST in the underlying graph of a network has the practical application of protection routing on fault-tolerance, it has been proved that determining whether a graph G admits a dual-CIST is NP-complete. As we know that Cayley graphs are a large family of graphs, some of its subclasses have been attracted and thus graphs in these subclasses have been adopted as the topologies of interconnection networks, such as the n-dimensional star graphs $S_n$, bubble sort graphs $BS_n$, pancake graph $P_n$, alternating group networks $AGN_n$ and so on. Pai and Chang (IEEE/ACM Trans Netw 27(3): 1112–1123, 2019) recently showed that there exist dual-CISTs in $S_n$, $BS_n$, $AGN_n$ for $n\geqslant 5$ and provided their corresponding protection routings. So far, the problem of constructing dual-CISTs on $P_n$ has not been dealt with yet. In this sequel, we continue the investigation of the construction of dual-CISTs in pancake graphs as a complementary result. Since $P_n$, $S_n$, and $BS_n$ are with the same scale, we experimentally assess the performance of protection routing through simulation results for comparing them when $n=5,6,7$.