We present the communication lower bound for the prefix problem on a multip
ort message-passing fully connected multicomputer. Two efficient parallel p
refix algorithms are also presented. Both are optimal in the number of comm
unication steps. One of them is also time-optimal; the other is cost-optima
l when n = Omega(p log p), where n is the input size and p < n is the numbe
r of processors used. (C) 1999 published by Elsevier Science B.V. All right
s reserved.