Fault-tolerant routing on the star graph with safety vectors

The concept of safety vector can guide efficient fault-tolerant routing on interconnection networks. The safety vector on the hypercube is based on the distance of a pair of nodes. However, the distance measure cannot be a lied on star graphs directly, since there are many routing path patterns when the distances of two pairs of nodes are the same. Thus, on star graphs, we define the safety vector based on the routing path patterns. Based on the concept of routing path patterns, we first define the undirected safety vector, which is a one-dimensional vector on each node. In addition, we propose some methods for solving some problems on the safety vectors of the star graph, such as the length of safety vectors and the ranking of the routing path patterns.