Optimal deterministic approximate parallel prefix sums and their applications

We show that extremely accurate approximation to the prefix sums of a sequence of n integers can be computed deterministically in O(log log n) time using O(n/log log n) processors in the COMMON CRCW PRAM model. This complements randomized approximation methods obtained recently by Goodrich, Matias and Vishkin, (1993) and improves previous deterministic results obtained by Hagerup and Raman. Furthermore, our results completely match a lower bound obtained recently by Chaudhuri. Our results have many applications. Using them we improve upon the best known time bounds for deterministic approximate selection and for deterministic padded sorting