An efficient adaptive routing algorithm for the faulty star graph

This paper introduces an adaptive distributed routing algorithm for the faulty star graph. By giving two routing rules based on the properties of nodes, an optimal routing function for the fault-free star graph is presented. For a given destination in the n-star graph, n-1 node-disjoint and edge-disjoint subgraphs, which are derived from n-1 adjacent edges of the destination, can be constructed by applying this routing function and the concept of breadth first search. When faults are encountered, the algorithm can route messages to the destination by finding a fault-free subgraph based on the local failure information. As long as the number f of faults (node faults and/or edge faults) is less than the degree n-1 of the n-star graph, the algorithm can adaptively find a path of length at most d+4f to route messages successfully from a source to a destination, where d is the distance between two nodes.