Efficient parallel prefix algorithms on fully connected message-passing computers

Given n values /spl nu/(0), /spl nu/(1), ..., /spl nu/(n-1) and an associative binary operation, denoted by o, the prefix problem is to compute the n prefixes /spl nu/(0) o /spl nu/(1) o...0 /spl nu/(i), 0/spl les/i/spl les/n-1. We are interested in prefix computation on message-passing fully connected multicomputers, in which each processor can only send or receive a message to or from any other processor in a communication step, in as few communication steps as possible. An algorithm is presented to solve the prefix problem on a system of n processors in no more than [1.44 log/sub 2/ n]+1 communication steps. Then, to explore the possibility of obtaining a faster algorithm, a class of algorithms is presented, It is shown that the algorithm in this class requiring the fewest communication steps is equivalent to the first algorithm presented. An algorithm using p