Binomial-Tree Fault Tolerant Routing in Dual-Cubes with Large Number of Faulty Nodes

A dual-cube DC(m) has m + 1 links per node where m is the degree of a cluster (m-cube), and one extra link is used for connection between clusters. The dual-cube mitigates the problem of increasing number of links in the large-scale hypercube network while keeps most of the topological properties of the hypercube network. In this paper, we propose efficient algorithms for finding a nonfaulty routing path between any two nonfaulty nodes in the dual-cube with a large number of faulty nodes. A node v ∈ DC(m) is called k-safe if v has at least k nonfaulty neighbors. The DC(m) is called k-safe if every node in DC(m) is k-safe. The first algorithm presented in this paper is an off-line algorithm that uses global information of faulty status. It finds a nonfaulty path of length at most d(s, t) + O(k) in O(|F | + m) time for any two nonfaulty nodes s and t in the k-safe DC(m) with number of faulty nodes |F | < 2(m + 1 − k), where 0 ≤ k ≤ m/2. The second algorithm is an online algorithm that uses local information only. It can find a faultfree path with high probability in an arbitrarily faulty dual-cube with unbounded number of faulty nodes.