Fault Covers in Rectangular Arrays

Abstract

The covering approach is used most frequently in rectangular arrays with spare rows and columns. Several examples of such architectures, including reconfigurable random access memories (RRAMs) and processor arrays, were described in Chapter 1. Recall that such architectures comprise an m × n array with S R spare rows and S C spare columns in which each faulty element is replaced by replacing the entire row in which it resides by a spare column. As we have mentioned in Chapter 1, the problem of finding a covering assignment for a faulty array is NP-complete [46]. Consequently, efforts in this area have been in the design of heuristics and exhaustive search algorithms. Heuristics can generally find solutions in a short amount of time, but may not always find solutions when they exist. In contrast, exhaustive search algorithms can always find solutions when they exist, but may require exponential running time in the worst case. In this chapter we propose new techniques that can significantly reduce the running time of exhaustive search algorithms for many of these problems.