Extended-Fault Diameter of Mesh Networks

The diameter of a network in the presence of faulty nodes is an important indicator of its resilience. Certain popular topologies have been shown to possess fault diameters that are only one unit greater than those of the corresponding fault1ree networks, provided that the number of faults is strictly less than the network's connectivity. Examples of such robust networks include hypercubes, m-ary q-cubes, cubeconnected cycles, and star graphs. We derive the extended-fault diameter of mo x ml x ... x mq-l mesh networks. Mesh networks, which play an important role in the implementation of parallel processors are not node-symmetric (even when all the mi are equal) and thus do not easily lend themselves to theoretical analyses; hence, the fault diameter of meshes has not been previously dealt with. Furthermore, we do not require the number of faults to be less than the network's connectivity, as has been done in previous studies. Such a requirement would limit the number of faulty nodes to 1 in the case of 2D meshes, which is unduly restrictive. Hence, our motivation to define and study a network's extended1ault diameter.