A routing and broadcasting scheme on faulty star graphs

Abstract

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 e cient broadcast algorithm on the star graph in the presence of faults.

Strong Fault-Tolerance: Parallel Routing in Networks with Faults

“…The general fault tolerance properties of the star networks were first studied and analyzed in [1,2,3]. Algorithms for singlepath routing in star networks with faults were developed in [4,11,17]. Parallel routing algorithms on the star networks were studied in [10,9].…”

Fault Tolerance on Star Graphs

“…The fault-tolerant routing algorithm proposed by Bagherzadeh et al [5] is based on the depth first search strategy. The major overhead of this kind of algorithm is backtracking.…”

“…The routing algorithm on faulty star graphs is proposed by Bagherradeh et al [5], which is based on the greedy routing algorithm combined with depth first search [ 2 , 6 ] . When there are at most n -2 faults, the algorithm has penalty O(&.…”

AN ADAPTIVE HEURISTIC ALGORITHM WITH THE PROBABILISTIC SAFETY VECTOR FOR FAULT-TOLERANT ROUTING ON THE (n, k)-STAR GRAPH

“…Several fault-tolerant routing algorithms on S n have been proposed [2,8,14]. It requires some new approaches to record the accessibility of each node to assist us for routing on S n,k .…”