A simple optimal list ranking algorithm

We consider the problem of ranking an N element list on a P processor EREW PRAM. Recent work on this problem has shown the importance of grain size. While several optimal O(N/P+log P) time list ranking algorithms are known, Reid-Miller and Blelloch (1994) recently showed that these do not lead to good implementations in practice, because of the fine-grained nature of these algorithms. In Reid-Miller and Blelloch's experiments the best performance was obtained by an O(N/P+log/sup 2/ P) time coarse grained randomized algorithm devised by them. We build upon their idea and present a coarse-grained randomized algorithm that runs in time O(N/P+log P), and is thus also optimal. Our algorithm simplifies some of the ideas from [6, 7]-these simplifications might be of interest to implementers.