A fault-tolerant adaptive and minimal routing approach in 3-D meshes

We propose a sufficient condition for minimal routing in 3-dimensional (3D) meshes with fault nodes. Unlike many traditional models that assume all the modes know global fault distribution or just adjacent fault information, our approach is based on the concept of limited global fault information. First, we propose a fault model called faulted cube in which all faulty nodes in the system are contained in a set of faulty cubes. Fault information is then distributed to limited number of nodes while it is still sufficient to support minimal routing. The limited fault information collected at each node is represented by a vector called extended safety level. The extended safety level associated with a node can be used to determine the existence of a minimal path from this node to a given destination. Our results show that any minimal routing that is partially adaptive can be applied in our model as long as the destination node meets a certain condition. We also propose a dynamic planar adaptive routing scheme that offers better fault tolerance and adaptivity than the planar adaptive routing scheme in 3D meshes. Our approach is the first attempt to address adaptive and minimal routing in 3D meshes with faulty nodes using limited fault information