Dual Protection Routing Trees on Graphs

In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. He then showed that "whether there is a protection routing to the destination" is NP-complete. Tapolcai found that two completely independent spanning trees, abbreviated as CISTs, can be used to configure the protection routing. In this paper, we proposed dual protection routing trees, denoted as dual-PRTs to replace CISTs, which are less restrictive than CISTs. Next, we proposed a transformation algorithm that uses dual-PRTs to configure the protection routing. Taking complete graphs K-n, complete bipartite graphs K-m,K-n, hypercubes Q(n), and locally twisted cubes LTQ(n) as examples, we provided a recursive method to construct dual-PRTs on them. This article showed that there are no two CISTs on K-3,K-3, Q(3), and LTQ(3), but there exist dual-PRTs that can be used to configure the protection routing. As shown in the performance evaluation of simulation results, for both Q(n) and LTQ(n), we get the average path length of protection routing configured by dual-PRTs is shorter than that by two CISTs.