Unsafety vectors: A new fault-tolerant routing for the binary n-cube

This paper presents a new fault-tolerant routing algorithm for the binary n-cube which overcomes the limitations of the recently-proposed safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321). The algorithm is based on the concept of "unsafety vectors". Each node A starts by computing a first level unsafety set, S₁^A, composed of the set of unreachable neighbours. It then performs (m - 1) exchanges with its neighbours to determine the k-level unsafety set, S_k^A, for all 1 ≤ k ≤ m, where m is an adjustable parameter between 1 and n. S_k^A represents the set of all nodes at Hamming distance k from node A which are faulty or unreachable from A due to faulty nodes (or links). Equipped with these unsafety sets, each node calculates unsafety vectors, which are then used to achieve an efficient fault-tolerant routing in the binary n-cube. The kth element of the unsafety vector of node A represents a measure of the routing unsafety at distance k from A. We present an analytical study proving some properties of the proposed algorithm. We also conduct a comparative analysis through extensive simulation experiments that reveal the superiority of the proposed algorithm over the safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321) in terms of different performance measures, e.g. routing distances and percentage of reachability.