What designers of wafer scale systems should know about local sparing

Local sparing is a simple way to organize the redundancy of a fault tolerant system. Any system can be locally spared. Furthermore, local sparing preserves both regularity and planarity. In spite of this, the potential usefulness of local sparing appears to have been overlooked. Suppose that the designer wishes to assure, with high probability, a fault-free copy of the n-element system desired. If local sparing is used then, as proved, i) the resulting area is Θ(log n) times the area of the system desired; ii) the wire length is 𝒪(√(log n)) times the maximum wirelength in the desired system; iii) an optimal diagnosis algorithm identifies the faulty elements in Θ(n log² n) time; iv) in optimal time Θ(n log n+number of wires in the desired system), a simple configuration algorithm achieves a fault-free copy of the desired system if and only if a fault-free copy exists. The authors illustrate these results for arrays, binary trees, and hypercubes. In addition, v) if Y denotes the probability of achieving a fault-free copy of the system desired then, using h-fold redundancy, the maximum rate at which elements can fail is ((-ln Y)/n)¹h/. Local sparing is simple, widely-applicable, and low-cost. A disadvantage is that, depending on the system desired, the cost may not be optimal. However, there is strong reason to prefer local sparing over global sparing, and in some cases local sparing is better than more popular approaches to configuration