Finding maximal submeshes in 2D mesh in the presence of failed nodes

In a parallel computer system with faulty processors, it is highly desirable to reconfigure the system by eliminating the faulty ones and thereby restore the system to some operational state. In the reconfiguration finding the maximum size fault-free subsystem is the main problem. We propose an efficient scheme for identifying maximum size fault-free submeshes in a faulty two-dimensional (2D) mesh system. For this, the relations between two submeshes in a 2D mesh have been defined. Then we take a two phase approach. In the first phase, an efficient algorithm for determining maximal faulty submeshes in a faulty mesh has been introduced. In the second phase, we have introduced a procedure to identify the maximal fault-free submeshes by splitting all faulty submeshes from a whole mesh. The time complexity of the proposed scheme is O(N_f²) where N_f is the number of faulty processors in a 2D mesh. The proposed scheme can be utilized to the task allocation in 2D meshes in the presence of failed nodes