Fault-tolerant routing on the star graph with safety vectors

The concept of a safety vector can guide efficient fault-tolerant routing on interconnection networks. The safety vector on a hypercube is based on the distance between a pair of nodes. However, the distance measure cannot be applied on star graphs directly, since there are many routing path patterns when the distances between two pairs of nodes are the same. Thus, on star graphs, we define the safety vector based on the routing path patterns. Based on this concept of routing path patterns, we first define an undirected safety vector, which is a 1D vector on each node. In addition, we propose some methods for solving some problems concerning the safety vectors of the star graph, such as the length of the safety vectors and the ranking of the routing path patterns.