A Routing and Broadcasting Scheme on Faulty Star Graphs

In this paper we present a routing algorithm that uses the depth rst search approach combined with a backtracking technique to route messages on the star graph in the presence of faulty links. The algorithm is distributed and requires no global knowledge of faults. The only knowledge required at a node is the state of its incident links. The routed message carries information about the followed path and the visited nodes. The algorithm routes messages along the optimal, i.e., the shortest path if no faults are encountered or if the faults are such that an optimal path still exists. In the absence of an optimal path, the algorithm always nds a path between two nodes within a bounded number of hops if the two nodes are connected. Otherwise, it returns the message to the originating node. We provide a performance analysis for the case where an optimal path does not exist. We prove that for a maximum of n ? 2 faults on a graph with N = n! nodes, at most 2i + 2 steps are added to the path, where i is O(p n). Finally, we use the routing algorithm to present an eecient broadcast algorithm on the star graph in the presence of faults.