Good processor identification in two-dimensional grids

Abstract

We examine the problem of identifying good processors in self-testing two-dimensional grid systems. The grids have boundaries (not wrap-around) and degree 8. Our diagnostic objective is to identify at least one fault-free processor. From this, at feast one faulty processor could be identified and it would be possible to sequentially diagnose the system by repeated repair. We establish an upper bound on the worst case maximum number of faults while still being able to meet the diagnostic goal with an ideal diagnosis algorithm. A straightforward ideal diagnosis algorithm would have exponential complexity and would involve 16 parallel rounds of processor testing. We give a test schedule with at most 6 parallel rounds of testing. This test schedule tolerates asymptotically as many faults as an ideal algorithm (by a constant factor). The new test schedule will also work for grids with degree 4, which have inferior diagnostic potential.