Algorithm for constructing fault-tolerant solutions of the circulant graph configuration

Recently, a general method was developed to design a k-fault-tolerant solution for any given circulant graph, where k is the number of faulty nodes to be tolerated. In this paper, a new algorithm is proposed which, (unlike the earlier method), constructs a family of k-fault-tolerant solutions, for any given circulant graph. These solutions can then be compared to select the one with the least cost. The algorithm is efficient to implement as it requires only a polynomial time (to generate and search the solutions). The proposed method is also useful to other architectures, as demonstrated in the paper. We shall examine the application of the method to the problem of designing k-fault-tolerant extensions of (2 and 3 dimensional) meshes, and show that the solutions obtained are very efficient