Three Completely Independent Spanning Trees of Crossed Cubes with Application to Secure-Protection Routing

Kwong et al. (2011) proposed a reactive routing scheme using the multi-paths technique for integrating two mechanisms of route discovery and route maintenance in intra-domain IP networks. They further defined a routing to be protected if there is a loop-free alternate path for packet forwarding when a single link or node failure occurs. Later on, Tapolcai (2013) showed that a network possessing two completely independent spanning trees (CISTs for short) suffices to configure a protection routing. A set of k(≥ 2) spanning trees in a network is called CISTs if they are pairwise edge-disjoint and inner-node-disjoint. Particularly, if k=2, such a set of CISTs is called a dual-CIST. Hasunuma (2002) pointed out that determining if there exists a dual-CIST in a graph is an NP-hard problem. In this paper, we investigate how to construct CISTs in a kind of hypercube-variant networks, called crossed cubes, and obtain the following results: (1) The crossed cube CQ_n for n ≥ 6 admits three CISTs. (2) We demonstrate that protection routing is also suitable for relatively large (static) network topologies with scalability, such as interconnection networks with recursive structure. (3) We configure a protection routing in crossed cubes such that all messages transmitted in the network are secure, i.e., no other node except the destination can receive the complete message.