Applying fault-tolerant solutions of circulant graphs to multidimensional meshes

Recently, circulant graphs have received a lot of attention; and a new method was proposed for designing fault-tolerant solutions for any given circulant graph. This method works by partitioning the offsets of the graph in many ways; each leads to one or more solutions. By comparing all these solutions, we can find the one with the least node-degree. In this paper, we shall first review this method; and then re-examine its applications to the design of k-fault-tolerant meshes (for all possible values of k). Our results demonstrate that the solutions obtained (for both two and three-dimensional meshes) are efficient.