Reliable Computations on Faulty EREW PRAM

We consider the problem of efficient and reliable computing on EREW PRAM whose processors are subject to random independent stop-failures with constant probability p < 1. An algorithm for such a fault-prone machine is called safe if it solves a problem of size n with probability exceeding 1 d/n, for some constant d independent of n. Our main contribution is a safe algorithm for the well-known list ranking problem, working in time O(logn) on an O(n log n)-processor EREW PRAM. We also show an optimal safe algorithm for computing prefix sums, which works in time O(log n) on an O(n/ log n)-processor EREW PRAM. The methods presented in this paper can be applied to a wide class of EREW PRAM algorithms making them safe and simultaneously preserving their complexity.