A new approach for routing in arrangement graphs and its performance evaluation

Abstract

We consider only the case of faulty links, but it can be extended to the case of faulty nodes by following a similar procedure. Our algorithm has two novel features: it looks for not only optimal paths but also near-optimal paths, and it intends to find an optimal node mainly. We believe that it is a useful tool for improving the efficiency of routing algorithms, specially when the information that every node possesses is limited. We also show the mathematical expression for the probability of routing messages via an optimal path for any pair of nodes. We consider that the source and destination are at maximun distance to illustrate our results. It is shown that the algorithm routes messages via optimal paths with very high probability, that enhance the excellent properties for communication of (n, k)-arrangement graph.