Efficient and optimal fault-to-spare assignments in doubly fault tolerant arrays

Given a doubly fault tolerant system with m faults, the authors present an algorithm for finding a fault-to-spare assignment for the m faults in O(m) time. This improvement over the O(m^1.5) bi-partite graph technique for finding an assignment is obtained by partitioning the problem into independent regions and proving that, in each region, an assignment may be found in linear time. The region approach also allows for an efficient solution of a related problem. Namely, finding a fault-to-spare assignment which minimizes the number of uncovered nodes. For two dimensional arrays augmented with one row and one column of spares, such an optimal assignment may be found in linear time