Improved parallel integer sorting without concurrent writing

We show that n integers in the range 1, ..., n can be sorted stably on an EREW PRAM using O(t) time and O(n(root log n log log n + (log n)(2)/t)) operations, for arbitrary given t greater than or equal to log n log log n, and on a CREW PRAM using O(t) time and O(n(root log n + log n/2(t/log n))) operations, for arbitrary given t greater than or equal to log n. In addition, we are able to sort n arbitrary integers on a randomized CREW PRAM within the same resource bounds with high probability. In each case our algorithm is a factor of almost Theta(root log n) closer to optimality than all previous algorithms for the stated problem in the stated model, end our third result matches the operation count of the best previous sequential algorithm. We also show that n integers in the range 1, ..., m can he sorted in O((log n)(2)) time with O(n) operations on an EREW PRAM using a nonstandard word length of O(log n log log n log m) bits, thereby greatly improving the upper bound on the word length necessary to sort integers with a linear time-processor product, even sequentially. Our algorithms were inspired by, and in one case directly use, the fusion trees of Fredman and Willard. (C) 1997 Academic Press.