Improved Parallel Integer Sorting without Concurrent Writing

Susanne Albers, Torben Hagerup
1997 Information and Computation  
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(-log n log log n+(log n) 2 Ât)) operations, for arbitrary given t log n log log n, and on a CREW PRAM using O(t) time and O(n(-log n+log nÂ2 tÂlog n )) operations, for arbitrary given t 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 3(-log n)
more » ... r to optimality than all previous algorithms for the stated problem in the stated model, and 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 be 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. ] 1997 Academic Press 25 0890-5401Â97 25.00
doi:10.1006/inco.1997.2632 fatcat:lfxceubgffazhdbhgthfd5rxim